Healthcare Access, Costs, and Treatment Dynamics: Evidence

from In Vitro Fertilization∗

Barton H. Hamilton

Washington University in St. Louis

Olin Business School

Emily Jungheim

Washington University in St. Louis

School of Medicine

Brian McManus

University of North Carolina-Chapel Hill

Department of Economics

Juan Pantano

University of Chicago

Center for the Economics of Human Development

March 12, 2018

Abstract

We study public policies designed to improve access and reduce costs for In Vitro Fertilization

(IVF). High out-of-pocket prices can deter potential patients from IVF, while active patients

have an incentive to risk costly high-order pregnancies to improve their odds of treatment

success. We analyze IVF’s rich choice structure by estimating a dynamic model of patients’

choices within and across treatments. Policy simulations show that insurance mandates for

treatment or hard limits on treatment aggressiveness can improve access or costs, but not both.

Insurance plus price-based incentives against risky treatment, however, can together improve

patient welfare and reduce medical costs.

Keywords: In Vitro Fertilization, insurance mandates, healthcare access and cost, pricingrisky behavior

JEL Codes: G22, I11, I13. I18, J13

∗Authors’ contact information: hamiltonb@wustl.edu, jpanta@uchicago.edu, mcmanusb@unc.edu,jungheime@wudosis.wustl.edu. We thank for comments and suggestions Jaap Abbring, Naoki Aizawa, GaryBiglaiser, Flavio Cunha, Liran Einav, Hanming Fang, George-Levi Gayle, Donna Gilleskie, Limor Golan, PedroMira, Bob Pollak, Jimmy Roberts, John Rust, Seth Sanders, Steve Stern, Xun Tang, Ken Wolpin, and participantsat several conferences and workshops. All errors are our own.

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1 Introduction

Healthcare policymakers struggle with the conflicting goals of providing ready access to medical

care while simultaneously containing costs. For example, in the U.K. a medical treatment may not

be covered by national insurance if it fails to meet a cost-effectiveness criterion. U.S. insurance plans

have focused on alternative cost-sharing arrangements as a means of influencing patient choice, but

the scope of such arrangements is limited due to relatively low out-of-pocket maximum payments

(Feldstein and Gruber, 1995). Optimal health insurance design suggests that a patient desiring an

expensive, technologically advanced treatment should face higher co-payments (e.g., Chernew et al.,

2000). In this spirit, recently introduced “value-based” insurance plans tie patient co-pays to the

clinical value of treatment (Chernew et al., 2007). Spurred by the Affordable Care Act, value-based

principles have been experimented with in primary care and pharmaceutical plans. However, such

insurance policies are still uncommon and few empirical studies (e.g. Einav et al., 2016) evaluate

the ability of treatment-dependent pricing to influence patient behavior and control costs.1

In this paper, we study the impact of alternative policies on patients’access to care, patients’

surplus, and healthcare costs in a context that embodies many of the features of more complicated

medical treatment: the market for In Vitro Fertilization (IVF) in the U.S. Over the last 20 years,

IVF use has increased four-fold to 160,000 treatment cycles annually, driven in part by delayed

fertility decisions by women.2 Because individual cycles of IVF treatment often fail, potential IVF

patients must solve a complex sequential decision problem under uncertainty about whether to

initiate and/or continue therapy.3 Patients (in consultation with their physicians) must also decide

on the type of treatment, based on their preferences and the cost of therapy. More aggressive treat-

ment increases the probability of pregnancy, thus reducing the need for additional IVF cycles, but

it also increases the risk of costly higher-order births. IVF patients now account for approximately

50% of all higher-order births, which are generally four (twins) to sixteen (triplets) times more

expensive than a singleton birth. Consequently, IVF resembles other medical treatments, like those

1Baicker et al. (2013) simulate the impact of an alternative to Medicare in which all individuals are guaranteedbasic benefits, but are provided the option to “top-up” by purchasing additional coverage for more expensive, lesscost-effective treatments. Such a scheme may lead to more unequal healthcare spending but lower cost growth.

2 IVF currently accounts for 1% of U.S births. Treatment rates are even higher in some other countries; IVFaccounted for over 3% of 2011 births in Israel, Belgium, Sweden, and Denmark. The aggregate treatment statisticsreported in this paragraph for the U.S. are for fresh-embryo treatments during 2012, the most recent year for whichU.S. data are available (Centers for Disease Control and Prevention (CDC), 2014). Statistics from European countriesare from the European Society of Human Reproduction and Embryology’s (2014) ART Fact Sheet. Israel’s IVF birthshare is reported by Simonstein et al. (2014).

3Relatively young U.S. patients (under 35 years old) in 2012 achieved a birth after 40% of cycles, while patientsjust under 40 years old had success rates approximately half as large.

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for heart disease or cancer, where dynamic decisions are made across a variety of treatment steps

while health information is gradually revealed, and patients weigh the direct effects of alternative

treatment options against potential side effects (Chan and Hamilton, 2006).4

High out-of-pocket costs for IVF (typically $10,000 - $15,000 per cycle of treatment) and the

high rate of expensive multiple births have led policymakers to consider a variety of interventions in

the hopes of achieving two goals: improving IVF access in the population and reducing treatment

risks and costs. To increase access, ten U.S. states have mandated insurance coverage for IVF;

these policies endow each potential patient with several covered treatment attempts for an out-of-

pocket price of $2,000-$3,000. While mandates should lead to higher utilization rates, the policy

also has the potential to contain costs. This might be the case if patients, aware that future insured

attempts would also occur at a lower price, decide to engage in less aggressive treatment by taking

fewer embryos. Transferring more embryos increases both the probability of pregnancy and the

likelihood of a multiple birth. As the medical costs associated with birth are generally paid by

insurers, treatment aggressiveness may be described as moral hazard.

Concern about moral hazard and the high rate of costly multiple births has led some European

countries to limit the treatment options available to IVF patients in the form of an explicit cap on

the number of embryos transferred during treatment. U.S. medical experts have recently advocated

for embryo caps due to their perspective that a singleton birth is the best possible outcome of treat-

ment.5 While single embryo transfer nearly eliminates costly high-order births, it also substantially

reduces the odds of conception for each IVF attempt. Consequently, such restrictions will generally

affect the optimal treatment paths selected by forward-looking patients. An embryo restriction

effectively increases patients’expected discounted cost of conception, which can lead some patients

to forego IVF altogether or abandon treatment after initial failure, thus implicitly reducing access

to IVF.

To evaluate the impact of these and other alternative policies, we specify a structural model of

forward-looking, infertile patients’decisions to initiate and or/continue IVF treatment using fresh

4Medical treatment guidelines themselves traditionally have been static or open-loop. Murphy (2003) introducedthe notion of “optimal dynamic treatment regimes” to construct adaptive decision rules, and this framework hasbeen applied to physicians treating disease. Murphy’s approach builds on earlier work by Robins (1997) on dynamictreatment effects. Her approach, however, focuses on dose-response relationships and does not incorporate or estimatepatient preferences. This inhibits the study of settings where patients exercise some discretion over treatment protocol,and limits the focus to objective outcomes (e.g. biological responses) rather than also allowing subjective ones (e.g.welfare). Abbring and Heckman (2007) describe this area of the statistics literature, and they contrast the literature’sassumptions with structural econometric approaches that, as in our paper, rely on dynamic choice models.

5The Practice Committee for the Society for Assisted Reproductive Technology (2012) summarizes a number ofstudies on single embryo transfer and concludes that IVF clinics should promote elective single embryo transfer.

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non-donor eggs and embryos.6 Treatment choice dynamics for IVF patients reflect a number of

mechanisms. First, patients must consider both the current and future price of treatment because

outcomes are uncertain.7 Due to high potential future costs, patients may choose aggressive cur-

rent treatment that raises both the probability of pregnancy and the likelihood of a multiple birth.

Second, patients may expect their medical condition to change over time. Female fertility declines

with age, particularly after age 35, when many IVF patients receive treatment. Anticipation of fu-

ture health declines affects current decisions regarding both the initiation choice and aggressiveness

of treatment. As treatment choices are affected by intertemporal variation in prices, health, and

information, we expect that possible regulatory changes could have subtle impacts throughout the

decision process.8

We estimate the model using a novel dataset of the treatment histories of women undergoing IVF

at an infertility clinic (“the clinic”) between 2001 to 2009, as well as data on potential patients in the

St. Louis, Missouri, market where the clinic is located. This setting provides a valuable opportunity

to understand how prices, preferences, and health affect IVF treatment. The clinic serves patients

from both Illinois, which mandates insurance coverage of IVF, and Missouri, which does not.

Consequently, we are able to analyze the decisions of observationally equivalent patients facing

vastly different prices (about $3,000 for covered patients versus $11,000 for those without insurance)

undergoing the same procedure with the same physicians. Using highly detailed information on

the fertility attributes of the patients and their treatment choices and outcomes, we estimate the

various stochastic processes that determine success at each stage of an IVF treatment cycle. These

processes, together with the specifications of patient preferences over children and the disutility

from payments, yield a finite-horizon dynamic optimization problem that spans the reproductive

years of (otherwise) clinically infertile women. The model delivers policy functions that specify: a)

whether to initiate an IVF treatment, b) the treatment choices within an IVF cycle, and c) whether

(and when) the patient re-attempts to conceive through IVF. We estimate the empirical model in

three steps. The first step is the estimation of the treatment “technologies”determining outcomes6A large majority of IVF cycles use the patient’s own eggs (i.e. nondonor) and transfer embryos that were never

frozen.7As discussed below, insured patients may be concerned about exhausting their benefits, which raises future prices

for IVF. This is in contrast to other insurance scenarios in which patients initially experience high out-of-pocket costsfor treatment and then face low prices once their insurance deductible is reached. Aron-Dine et al. (2015) examine thedynamic implications of changes in out-of-pocket costs induced by exhaustion of deductibles. In a study of insurance’srole in risk protection and moral hazard, Kowalski (2015) accounts for the impact of deductibles, coinsurance, andstoplosses in consumers’nonlinear budget sets.

8Fang and Gavazza (2011) provide another example of the dynamic interaction between government policy andhealth choices and outcomes. They provide evidence that the US employer-provided health insurance system providesdisincentives to invest in health over the life-cycle.

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during the four stages of a given IVF cycle. The second step recovers the structural parameters

of our within-clinic patient decision model by maximizing the likelihood of the observed treatment

choice histories. These parameters indicate that patients prefer singleton and twin births to the

more dangerous triplet births, and the utility from additional children falls in the number of children

the patient already has. These estimates are necessary to assess how patients would respond to

policies designed to reduce treatment aggressiveness. The third step captures potential patients’

decisions to ever initiate treatment.

Due to the dynamic incentives and tradeoffs highlighted by our model estimates, we conduct

counterfactual experiments investigating the impact of alternative policy proposals on individual

patient actions, outcomes, and surplus. We first consider the widely-discussed policies of mandated

insurance coverage and treatment restrictions in the form of embryo caps. Relative to a baseline

case in which no women have insurance, introducing universal coverage for IVF results in more than

a doubling of the share of infertile women who initiate treatment (24% vs. 58%). This increase

in access is accompanied by an increase in consumer surplus from $2,700 to $6,600 per potential

patient. While insurance reduces the opportunity cost of failed treatment, which in principle could

affect embryo transfer rates, we find only a small reduction in treatment aggressiveness because

our estimates imply that patients receive about the same utility from singleton and twin births,

implying little reason to transfer fewer embryos. Therefore, while this policy succeeds at increasing

access, it is of little help in terms of cost control. In an effort to contain costs, we next evaluate the

policy of a “European-style”treatment restriction combined with universal insurance. The strictest

policy is a hard limit of one embryo per patient per cycle, which pushes treatment initiation down

to its no-insurance level, but with greatly reduced total costs and aggregate births. In terms of

costs per birth, however, the embryo cap is actually more expensive than the no-insurance baseline

due to low birth rates.

Given the cost growth induced by universal insurance, and the consumer surplus losses associ-

ated with treatment restrictions, we explore pricing schemes closer to those suggested by theoretical

models of optimal insurance design. While current practice in IVF allows patients to increase the

number of embryos at zero additional price, the full social cost of additional embryos is positive due

to the increased medical costs of higher-order pregnancies. Consequently, we evaluate the introduc-

tion of a value-based plan in which insured patients face “top-up prices”when transferring more

than one embryo.9 We select top-up prices that cover the (expected) increase in medical expense

9Einav et al. (2016) consider a closely related policy of top-up prices for medical care beyond a basic level covered

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relative to single-embryo transfers to minimize this potential source of moral hazard. Under the

top-up policy, patients reduce but do not eliminate multiple-embryo transfers, reflecting both a

preference for twin births and the incentive to reduce lifetime treatment costs. The presence of

insurance allows utilization (32%) to be greater than the no-insurance baseline, but with signifi-

cantly lower costs per birth ($63,100 per delivery versus $69,400 under the baseline), due to patient

payments against birth expenses and a reduction in multiple birth rates.10 In fact, total insurance

payments are lower with actuarially fair top-up prices and therefore insurance companies might be

content with insurance mandates that allow top-up price designs similar to those we analyze.

While insurance coverage for IVF in the U.S. is generally proposed as protection against the

high costs of infertility treatment, Israel takes a different approach by insuring birth outcomes

directly to encourage family formation. In particular, Israel allows unlimited IVF attempts until

the patient has two or more children. Our final set of counterfactuals compares such outcome-based

insurance designs with more traditional policies that provide a fixed number of treatments. We

find that an outcome-focused policy has nearly identical patient benefits and costs as mandated

universal insurance coverage found in U.S. states such as Illinois. The Israeli design also highlights

the dynamic impacts of IVF policies. We show that age-related limits on the Israeli policy leads to

welfare and choice differences related to patients anticipating future reductions in policy generosity.

The remainder of the paper proceeds as follows: Section 2 provides a preview of the four stages of

an IVF treatment cycle, and describes state level policies governing insurance coverage of infertility

treatment. Section 3 covers assumptions on model components, which are incorporated into our

dynamic structural model of treatment choice developed in Section 4. In Section 5 we describe

the data we obtained from the clinic, plus additional market-level data. Section 6 discusses the

empirical specification of our model and Section 7 provides estimation details. Section 8 presents

the parameter estimates and measures of model fit, and Section 9 contains the results from our

counterfactual policy simulations. Conclusions follow.

by insurers.10Greater IVF access can be achieved with smaller top-up prices, if desired.

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2 IVF overview and our setting

2.1 IVF background

A couple is defined to be medically infertile if they are unable to conceive after attempting to do

so for 12 months. Initial treatment for infertility often includes the use of the drug clomiphene to

induce ovulation, or the use of hormone shots with or without intrauterine insemination. While

such treatments are relatively low cost, they are less effective than more technologically advanced

treatments, more likely to lead to higher order pregnancies, and can be especially poorly suited to

older patients and those with male factor infertility. Due to these limitations, couples may choose

to directly undergo IVF. Others may eventually turn to IVF after failing to conceive through these

less advanced treatments.

Once a patient has decided to use IVF, the treatment cycle unfolds in stages. First, the woman

takes drugs to stimulate egg production. The patient and doctor monitor the response to these

drugs and may choose to cancel the cycle if the patient’s response is not favorable; if a cycle is

cancelled, the patient may start IVF again in the future. If the cycle is not cancelled, the eggs are

retrieved during a minor surgical procedure and then fertilized in the laboratory. The doctor may

recommend the use of intracytoplasmic sperm injection (ICSI), in which a single sperm is injected

into the egg. ICSI was initially used to address male-factor infertility problems, but has become

more widely used. The patient then decides how many fertilized eggs (cleavage-stage embryos) to

transfer to the womb; this choice may be constrained by the number of embryos that develop. At

this point the patient faces an important tradeoff: the probability of a live birth increases with

the number of embryos transferred, but so does the likelihood of a potentially costly and medically

risky multiple birth. Lemos et al. (2013) calculate that the average medical cost of a singleton

IVF pregnancy and initial child medical care is $26,922, while twin and triplet births entail costs of

$115,238 and $434,668, respectively.11 The high costs of multiple births are due largely to shorter

gestation periods, which can lead to newborns being admitted to neonatal intensive care units. The

medical costs calculated by Lemos et al. (2013) are typically not paid in full by the IVF patient

herself, so they introduce the possibility of moral hazard to the embryo transfer decision.12

11Lemos et al. (2013) obtained a sample from MarketScan of 437,924 deliveries covered by commercial insuranceover the period 2005-2010 to derive their cost figures. Approximately 6,500 of these deliveries were IVF-relatedpregnancies. Reported costs were the sum of mother’s medical expenses from 27 weeks prior to delivery to 30 daysafter, plus infant medical expenses up to the first birthday. Average health care costs were $5,510 (singleton) to$27,469 (triplet) higher for IVF pregnancies compared to other births.

12Some medical conditions associated with early births can require life-long medical care, but we do not considerthat care’s costs in this paper.

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If the IVF cycle does not result in a live birth, the patient then must decide whether (and

when) to attempt another cycle of treatment. Anticipation of future opportunities to receive IVF

is an important part of a patient’s decisions during the current IVF cycle. Because fertility declines

with age, subsequent cycles are less likely to be successful, all else equal, and couples potentially

incur substantial out-of-pocket cost if they try again. Patients whose treatments succeed may also

try IVF again if they want to add more children to their families. More broadly, there exists some

survey evidence (Hojgaard et al., 2007; Ryan et al., 2004) which suggests that patients may prefer

a twin birth to a singleton. This preference could be motivated by a variety of factors, including

declining fertility with age and the view that a twin birth is a cost-effective way to achieve a goal

of multiple children.

2.2 Public policy and analysis of its impact

A key feature of the U.S. market for IVF is the presence of state-level mandates regarding whether

and how insurers must offer coverage for infertility treatment, including IVF. During the period

of our study, 2001-2009, seven states had mandates requiring some form of insurance coverage for

IVF. Connecticut (after 2005), Illinois, Massachusetts, New Jersey, Rhode Island had the strongest

mandates for IVF, requiring insurers to cover a certain number of IVF treatment cycles.13 Prior

empirical research on insurance mandates has used a variety of approaches to examine issues related

to IVF access, embryo transfer patterns, and birth outcomes. The distinguishing feature of the

past research is that potential patients’activity and outcomes are examined in aggregate, either

at the population or clinic level. Schmidt (2005, 2007), Bitler (2008), Bundorf et al. (2008),

and Buckles (2013) examine the impact of insurance mandates on population-level fertility rates,

multiple birth rates, and child health. Hamilton and McManus (2011), Jain et al. (2002), and

Henne and Bundorf (2008) investigate the impact of mandates on the number of patients served,

embryo-transfer patterns, and birth outcomes at IVF clinics. Bitler and Schmidt (2006, 2012)

use survey data to examine similar issues. While patient-level decisions and characteristics play a

central role in generating the aggregate activity studied in these papers, their empirical approaches

do not allow a direct examination of choices, counterfactual experiments, or welfare effects.14

An additional policy proposal, motivated by the goal of reducing multiple births and their

13See Schmidt (2005, 2007). Maryland, Arkansas, Hawaii and Montana are also classified mandate-to-cover stateswhere the mandate includes IVF. Texas has a mandate requiring insurers to offer plans that include IVF coverage.Nothing prevents insurers, however, from charging substantially higher prices for plans that include this coverage.

14Some studies exist in the medical literature that use patient-level IVF data (e.g. Malizia, Hacker, and Penzias,2009), but their focus and approach are naturally different from our own.

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medical costs, is a single-embryo cap for IVF. While single embryo transfer is uncommon in the

United States (only 10% of IVF cycles in 2009 involved a transfer of one embryo), it is widely

practiced in Europe. For example, 69% of IVF cycles in Sweden transfer a single embryo and

in Belgium it is required. The prior literature on this policy has focused on the medical impact

of single-embryo transfers, whether voluntary or by rule. For examples, see Ryan et al. (2007),

Jungheim et al. (2010), Csokmay et al. (2011), or Velez et al. (2014). By contrast, our focus

on individual utility-maximizing patients allows us to consider treatment initiation decisions and

patient welfare in addition to the impact of an embryo cap on multiple birth rates and medical

costs. Patient initiation and welfare are likely to be affected by a cap because additional (costly)

cycles are needed, in expectation, to achieve a pregnancy, and because some patients may prefer

twin outcomes to singletons births.

2.3 The clinic we study and its market

In order to put our study of a single IVF clinic in context, we assess how the clinic and market

we study compares to the full U.S. IVF market (Centers for Disease Control, 2014). In Table 1

we present some statistics on clinic characteristics during the sample period of 2001 to 2009. The

clinic we study was larger than the average U.S. clinic, with 370.2 cycles per year compared to the

U.S. average of 217.1 cycles. This may be due to the clinic’s position in a large research-oriented

hospital, which could both influence demand and facilitate the hiring of the clinic’s medical staff.

The median patient age in our sample is 34 years old, which is slightly below the national median.

The difference in patient age could be due to demographic patterns, or a response to insurance

coverage, which may encourage potential patients to try IVF more quickly following diffi culty

conceiving a child naturally. Patient health, as measured by the fraction of patients with multiple

female infertility diagnoses and the fraction of cases with a male infertility diagnosis, are similar

between the clinic we study and the national averages. Patient treatment choices over ICSI and

embryos transferred reflect less aggressive treatment in the clinic we study relative to the U.S.

averages. These treatment patterns, along with a greater birthrate per cycle (33.5% at the clinic

vs. 29.9% nationally), may be influenced by the difference in median patient age, which affects

both treatment choices and outcomes.

Turning to the clinic’s market, we examine how some critical demographic features compare to

the U.S. population. In our empirical analysis, we assume that potential patients are drawn from

all zip codes with centroids within 75 miles of our clinic. The area includes the city of St. Louis, its

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surrounding suburbs, and some rural towns outside of the metro area. This area captures almost

all of the patients who ever visit the clinic; a small number come from greater distances. Our model

accounts for age at first birth and wealth as measured through housing value. Fertility timing in

the St. Louis market is nationally representative: within the age range 22-44, the median maternal

age at first birth in 2001 was 31 in both the St. Louis metro area and nationally. We use zip code

median home value as a proxy for wealth. In the St. Louis MSA this value was $103,900 in the

year 2000, while nationally the value was slightly higher at $112,100. More specifically, 54.4% of

St. Louis-area women lived in zip codes with median home values above $100,000; nationally the

share was 56.7%. The market’s share of African American women ages 25-44 was 19.9% in 2000,

while the U.S. share was 13.3%.

Our study exploits the fact that the clinic draws patients from the greater St. Louis metro

area, which includes both Missouri, which has no insurance mandate, and Illinois, which has a

mandate. For patients in our study residing in Illinois and working for an employer covered by

the mandate, insurance plans are required to pay for up to 4 IVF cycles if the woman has no

children.15 This insurance coverage pays the majority of IVF costs, but about $3,000 in expenses

remain for insured patients due to co-payments and deductibles. For patients paying out-of-pocket

for IVF in our sample, the clinic charged about $11,000 per treatment cycle throughout the sample

period; this figure includes all drugs and medical procedures that are part of a complete IVF cycle.

The Illinois mandate exempts firms with fewer than 25 employees and organizations such as the

Catholic Church that may object to IVF for religious reasons. These individuals pay the full price

of IVF. Despite the absence of a mandate, some patients from Missouri have private insurance for

IVF; in these cases the clinic has found that IVF coverage details are similar to those of Illinois

patients. Some Missouri employers may choose to offer IVF coverage as a means to attract and

retain employees. We calculate that potential patients from Illinois are three times more likely

(30% versus 11%) to have IVF coverage than women from Missouri, but even in Illinois insurance

penetration is fairly low.

The patient-level information on insurance status allows us to exploit two sources of price

variation in this setting: cross-section variation is present through the locations of potential patients,

while longitudinal variation arises as patients exhaust their insurance coverage over the course of

multiple IVF cycles. We assume that St. Louis-area potential patients do not endogenously move

15 If the patient has already had a birth through IVF, the number of remaining covered cycles is set to 2. Thisimplies that an Illinois resident can have as few as three or as many as six covered cycles, depending on when orwhether she has a successful cycle.

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or change employers in order to receive mandated insurance coverage under Illinois’s IVF insurance

regulations.16

3 Model preliminaries

3.1 Timing

We consider two timing concepts in the model below. First, there are decision periods when active

patients choose whether to start or delay an IVF cycle. Second, in an IVF treatment cycle there are

four treatment stages during which patients make one choice per stage. The time unit of the model

is a 3-month period. We index the age of the patient (in 3-month periods) with a and calendar

time periods (also quarterly) with t, and we use j to index stages within a period during which

an IVF cycle is started. At each age a, within stage j, the patient selects an action yj,a from the

set Yj . The set Yj does not vary with a or t. Note that there will be two indexes, a and t, to keep

track of time-varying objects in the model; the primary index is “a.”Age is important because we

specify a finite horizon model, and also because age itself enters various stage technologies.

We assume that potential patients’ decisions begin with an exogenous event which prompts

them to consider having children. Women who are able to reproduce naturally (or with less tech-

nologically advanced infertility treatments) are immediately removed from the process we study in

this paper. The remaining women have reproductive diffi culties that can be solved by IVF only 17.

These women, who constitute our “at risk”population, evaluate the expected benefit of beginning

IVF relative to an outside option. The outside option, which we parameterize below, could include

adoption, surrogacy methods of reproduction, or remaining childless. If the woman does not begin

IVF at this critical moment, we assume she collects the value of the outside option and exits the

model permanently. We assume that policy changes that affect the value of pursuing IVF do not

change the value of this outside option.

Individual patients vary in the age at which they consider reproduction. We denote as a0 the

patient’s age (in quarters) when she considers IVF. The patient’s choice over IVF, if necessary,

arrives four quarters after her exogenous decision to first attempt reproduction, i.e. at age a−4.

16The typical patient takes two IVF treatments, which would provide up to $16,000 in savings on out-of-pockettreatment expenses. Individuals who seek these savings, however, could experience substantial monetary or utilitycosts related to job search and switching, housing search and switching, and potentially suboptimal matches in theIllinois labor and housing markets.

17Due to data limitations, we do not study the potential patient’s decisions of how quickly to turn to IVF, andhow this is affected by insurance coverage. We assume, instead, that all couples with fertility problems exhaust thesame set of alternatives before arriving at the IVF decision.

11

This timeline is consistent with a simplified setting in which all women believe themselves to be

fertile (but are unaware of their true infertility status) until their first pregancy attempt at age

a−4. A woman who is fertile conceives after 3 months of attempts and gives birth to her first baby

9 months later. An infertile woman experiences a year of unsuccessful pregnancy attempts until,

at age a0, she considers whether to pursue IVF and therefore become a patient at the clinic. If

at that point she opts to pursue IVF treatment, the patient may continue to make decisions until

a terminal age, amax. At this age the IVF clinic will no longer treat the patient and her birth

probability (via IVF or naturally) is zero.18 This allows a maximum of 4× (amax − a0 + 1) periods

for a patient whose reproductive decisions start at age a0. In our data we observe patients with

a0 between their late twenties and early forties. We define amin to be the youngest patient age

considered in our model. We set amin to be the first quarter of age 28, and amax is the final quarter

of age 44. Once a patient’s total number of children reaches 3 (or more), she automatically stops

making decisions within the model.

In addition to the age index, a time index (t) is useful for describing the data sample and

econometric procedure. This index is also necessary to describe the prevailing embryo-transfer

guidelines offered by the American Society for Reproductive Medicine (ASRM); these guidelines

changed once during our sample period, in 2004. Let ti,0 represent the period during which we first

observe patient i. We see a patient for the last time in Ti, which might be equal to amax or T ,

the end of the sample period. We assume that all treatment stages that follow from a treatment

starting in period t also occur in period t.

3.2 State variables and initial information

A patient who is considering treatment is aware of several personal characteristics that affect

treatment effectiveness and utility. There are two types of state variables in the model. First, there

are the state variables collected in the vector Z, which remain constant within periods but may

transition between them. Second, there are state variables which are revealed during the stages

of a treatment cycle, but do not carry over between periods. These variables include information

about treatment progress and additional taste shocks that affect the value of each treatment option

at a decision stage. We discuss these variables in detail below, when we introduce our model of

IVF treatment behavior.

18We assume this age upper bound for tractability. The clinic does not have a preset age limitation and, instead,evaluates each patient on a case-by-case basis.

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We divide the state vector Z into two parts. We track a patient’s age (a), a measure of her wealth

(zw), number of prior children (k), record of previous payments for IVF (zp), insurance status (ι),

and race (zr) in the state vector ZD.19 Some of these state variables are time-invariant and others

vary in how they evolve between periods. Age increases exogenously by three months every period.

Race is a permanent patient characteristic, and we assume wealth is constant also. We construct zw

with zip code-level data on housing values. We focus on patients with zero prior children (k = 0) at

the treatment initiation decision, and then k evolves endogenously as a controlled Markov process

which depends on treatment outcomes.20 Likewise, the patient’s record of prior IVF payments (zp)

and remaining insured cycles evolve endogenously according to the patient’s decisions within the

model. We initialize the number of insured cycles (ι) to four (the Illinois mandate value) for all

patients who ever use insurance, and this number falls by one whenever an insured patient advances

to the second stage of treatment, when eggs are removed during surgery.21 The forward-looking

patient is aware that IVF’s price increases substantially after her fourth insured cycle.

The second part of Z includes the patient’s biological characteristics, ZB. We assume that the

patient learns her own ZB if she initiates treatment. The characteristics in ZB include: the women’s

antral follicle count (AFC score, zafc), an indicator of her egg-producing ability; whether she has

one or more specific infertility diagnoses (zff ), e.g. endometriosis; and whether her partner has

male-factor infertility (zmf ). At the treatment initiation decision, the patient considers the possible

values of ZB she may have using the population frequency of these characteristics conditional on her

initiating age, fZB (ZB|a0). We assume that the distribution of ZB conditional on a0 is independent

of race.

Our assumptions on Z include a few simplifications that we impose to maintain tractability.

First, we do not allow patients to receive a detailed fertility screening before deciding to initiate

treatment, which could be used to reveal ZB. This is a simplification that abstracts away from real-

world opportunities for potential patients to learn about ZB during less sophisticated infertility

treatments or stand-alone screenings. We make this simplification in order to reduce the dimensions

of potential patient heterogeneity prior to treatment, and because of data scarcity about this

19Bitler and Schmidt (2006) document differences in infertility diagnoses and IVF usage across racial, ethnic, andsocioeconomic groups. Due to data limitations we consider a simple binary specification for zr, which records whethera woman is African American.

20All patients start with k = 0, and k evolves stochastically in each following period. The evolution of k dependson whether a cycle is started and what choices are made within that cycle. If no cycle is started or an ongoing cycleis cancelled, then ka+1 = ka. k remains constant as well if a cycle is unsuccessful. If a cycle at age a reaches theembryo transfer stage and at least one child is born as a result of that cycle (ka > 1) then ka+4 = ka + ka.

21We abstract away from some of the complicated details of the Illinois insurance code, discussed above.

13

heterogeneity among the population at large. Second, we assume that patients (and their doctors)

use no biological data other than ZB in choosing a treatment path for patients. We assume

that the patient’s observed biological state variables ZB and age fully capture her relevant fertility

characteristics; there are no unobserved state variables that directly affect treatment outcomes, and

previous cycles’choices and outcomes also have no direct impact on the current cycle’s outcomes.

As implied by this assumption, we do not model additional unobserved health characteristics which

the patient and her doctor learn about through IVF treatment itself.

Once the value of ZB is realized we consolidate notation and refer to the state vector Z =

[ZD, ZB]. In addition to acting as a state variable which influences treatment outcomes, patient

age also functions as a time index, so we add an ‘a’subscript to Z where appropriate. During an

arbitrary age Za = [ZDa , ZB], and at treatment initiation the state variables have the value Za0 .

We assume that the doctor knows how the variables in Za affect treatment outcome probabilities.

Each patient receives this information from her doctor and also knows her own preferences over

treatment outcomes.

3.3 Patients’preferences

Patients have preferences over birth outcomes (k), and these preferences can depend on the patient’s

existing number of children (k) at the start of an IVF cycle and other personal characteristics.

Possible values of k are in {0, 1, 2, 3}, and k takes values in {0, 1, 2}. (These values for k cover

98% of the patient population at the clinic.) We allow patients to have permanent unobservable

heterogeneity, indexed by τ . Let U(k|k, τ) represent the lump-sum utility payoff from a treatment

cycle that produces k children in that individual cycle, conditional on k prior children and τ . As a

normalization, we assume that treatment outcomes with k = 0 always result in U(k|k, τ) = 0 for

all patients. Beyond this normalization, we place no restrictions (e.g. concavity) on how U(k|k, τ)

changes with k; the restrictions, if present, could have the effect of imposing risk preferences over

values of k. While we treat U(k|k, τ) as a lump-sum benefit, we interpret it as the expected

utility from having k additional children, which may include health risks from high-order births.

The utility from children in U(k|k, τ) is policy-invariant. Other aspects of the model, introduced

below, may change due to policies we consider, and these can impact the forward-looking patient’s

continuation value from different birth outcomes.

To maintain tractability, we combine U(k|k, τ) additively with other payoff-related terms in

an indirect intertemporal expected utility function. Patients undergoing treatment experience

14

disutility, scaled by α, from paying positive prices. When a patient pays p within treatment, she

has the immediate utility loss of αp. We allow the value of α to depend on a patient’s wealth, so

we write α(zw). This specification for the effect of p on utility is consistent with a model where

consumption of other goods enters additively into the utility, and there is a static budget constraint

that allocates income between consumption of other goods and IVF expenses.22 Likewise, a patient’s

price depends on her insurance status, so we write p(ι). An additional potential source of disutility

is in a patient’s choice to deviate from the American Society for Reproductive Medicine (ASRM)

guidelines for embryo transfers. During our sample period the ASRM generally recommended

against four-embryo transfers for all patients, and single-embryo transfers for older patients.23

We assume that a patient’s utility falls by η0 if she makes a choice outside of the guidelines,

with no penalty otherwise. We specify the function η(x, Za) to combine the penalty value and

the conditions under which it is applied, with x as the number of embryos and Za capturing the

contemporary ASRM guidelines and their relationship to the patient’s current age. We assume that

ASRM guidelines changes come as a surprise to decision-makers, i.e. patients always believe the

current policy environment is permanent. When the ASRM guidelines change, patients immediately

reoptimize their treatment plans for the current rules, and then resume the belief that the guidelines

will never change again.

The remaining parts of patients’ preferences include the value from starting versus delaying

an individual treatment and a terminal value. Relative to a baseline flow utility from delay that

is normalized to zero, we assume that patients receive the flow benefit (or cost) of us during any

period in which she begins IVF treatment. us can include any physical or psychological stress from

undergoing IVF. Patients’ terminal payoffs are captured by the parameter vector uT (zp), which

depends on her prior payments. The patient receives uT at age amax + 1 regardless of whether she

remains active in the model up until amax or if her decision process ends due to k + k ≥ 3 at some

earlier a.

At each treatment node, the patient’s benefit from the available options includes an additional

taste shock, ε, which represents heterogeneity in patient’s circumstances and preferences. Following

22We have access only to a time invariant, proxy measure of wealth, zw. Therefore, we chose not to include anintertemporal budget constraint and we do not treat wealth (assets) as a time-varying state variable. High wealthoperates in the model by changing α and thus altering the utility cost of reduced consumption of other goods.

23Prior to the September 2004 rule change, the ASRM recommended against single-embryo transfers for all patients,as well as four-embryo transfers for patients under age 35 and undergoing their first cycle. After the guidelineschanged in September 2004, the recommendation against four-embryo transfers was extended to all patients underage 38 regardless of cycle number, plus patients between ages 38 and 40 who were taking their first cycle. Theguideline revision also removed the recommendation against single-embryo transfers for patients under age 35 ontheir first cycle.

15

Rust (1987), for computational ease, we assume that ε is distributed i.i.d. type 1 extreme value

across patients, time periods, treatment stages, and alternatives within each stage. We offset Euler’s

constant so that E [ε] = 0.

Finally, we assume that patients discount future decision periods by the factor β. We assume

that all discounting occurs across periods, and not across treatment stages. Treatment options and

outcomes that occur t periods into the future are discounted by βt. We do not estimate β in this

paper, so we set its value equal to β = 0.97.24

3.4 Technology and prices

During each IVF stage, a patient makes a choice about treatment; possibly pays a price out-of-

pocket; and anticipates the outcome of a random process, the results of which are revealed before

the next choice occurs. We now review notation for these processes, i.e. the treatment technologies,

and the prices patients pay. We assume that the technologies did not change during the sample

period. This accords with the actual practice of IVF during the early 2000s.

For a patient who has committed to the first stage of IVF treatment, her personal characteristics

and drug regimen will yield a Peak E2 score (e) to be revealed at the start of stage 2. The score

is a signal of the patient’s success in generating eggs. During the first stage, however, the patient

knows only the distribution of possible e values rather than the signal’s realization. Let fe(e|Za)

represent the probability that a patient with characteristics Za receives a score with value e, which

takes positive integer values. Moving to the second stage, we denote as fr(r|e, Za) the probability

of successfully retrieving r eggs for a patient with Peak E2 score e and personal characteristics

Za. A patient with a greater value of r is more likely to generate a large number of embryos in

the next stage. Once the patient reaches the third IVF stage, she observes her value of r and

considers the distribution over possible numbers of embryos, denoted X, available for transfer,

which will be realized following her decision on fertilization method (m). We write this distribution

as fX(X|r,m,Za), and note that it may be shifted by r, m, and the patient’s state variables.

Finally, in stage four the patient considers the number of children (k) that will be born, which is

affected by the number of embryos transferred (x out of the realized X) and the patient’s Z values.

The distribution over realizations of k is fk(k|x, Za).

We specify the prices that patients may pay at three treatment stages. The price of action

24 In principle, the nonstationary nature of our model could allow for identification β. In practice, however, thisparameter is often very diffi cult to estimate so we chose to fix it at a conventional value.

16

y in stage j is py,j(ι). In the first treatment stage, uninsured patients pay ps,1 = $3,000 if they

choose the action ‘start’(s), while insured patients pay ps,1 = $1,000. The positive price for insured

patients is due to deductibles, co-payments, and co-insurance charges. Patients who continue (c)

treatment in stage 2 pay pc,2 = $6,000 if uninsured, and pc,2 = $2,000 if insured. The third-stage

option to use ICSI (m2) carries a price of pm2,3 = $2,000 for uninsured patients, and a price of zero

for insured patients. The final stage, embryo transfer, has zero price for all patients regardless of

the number of embryos transferred.

4 Decision model and value functions

We now describe how patient preferences and IVF technology come together into a multi-stage

decision process. Conditional on starting IVF treatment, a patient makes a series of choices regard-

ing the aggressiveness of her treatment and whether the treatment continues at all. The patient’s

current incentives are affected by her future treatment opportunities and prices. Along the way,

the patient uses information that is known at the start of treatment (e.g. age, current number

of children, basic fertility diagnoses) and information that is collected incrementally as treatment

progresses (e.g. the numbers of eggs retrieved and embryos available for transfer). See Figure 1 for

an illustration of the IVF treatment stages described below. The figure contains some notation on

utility payoffs that is introduced later.

Some notational conventions are common across stages. We writeWy,j(Za, εy,j,a) as the value of

choice y during stage j of a treatment cycle. This function accounts for: expectations over future

treatment outcomes, taste shocks in current and future stages, and optimal behavior in future

stages. Patients’values of Wy,j(Za, εy,j,a) depend on τ , but we suppress this term for notational

simplicity. Let W y,j be the systematic component of Wy,j(Za, εy,j,a), i.e. Wy,j net of the additive

preference shock εy,j,a. We then have

Wy,j(Za, εy,j,a) = W y,j(Za) + εy,j,a. (1)

The patient observes the realization of the vector εj,a before making her choice during stage j. The

patient’s value at the start of stage j is

Wj(Za, εj,a) = maxy∈Yj{Wj,y(Za, εy,j,a)} = max

y∈Yj{W y,j(Za) + εy,j,a}. (2)

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E [Wj(Za, εj,a)] represents the expected value from an optimal decision within treatment stage j,

before observing the realization of εj,a. Due to the extreme value assumption for ε, we can write

E [Wj(Za, εj,a)] with the inclusive value expression:

E [Wj(Za, εj,a)] = log

∑y∈Yj

exp[W y,j(Za)]

. (3)

We begin by focusing on the treatment stages that occur within IVF, after the patient has

learned her value of ZB. Later in this section we return to the initiation decision.

4.1 Stage 1: Start treatment vs. delay

In all periods after the initiation decision, patients who began IVF previously will return to stage

1 and choose between the actions start (s) and delay (d). If the patient starts treatment, she pays

the price ps,1(ι) out-of-pocket and begins a regimen of pharmaceuticals to promote egg production.

The value from starting a treatment cycle at age a isWs,1(Za, εs,1,a), and it includes the expected

value from continuing to the second stage of treatment (E [W2(Za, ε2,a)]); the utility normalization

relative to delay, us; the price of starting a treatment cycle, ps,1 (ι); and a taste shock, εs,1,a. The

value of the second stage depends on the realization of e (the Peak E2 score), but this is not known

during stage 1. The value from starting a treatment cycle at age a is then

Ws,1(Za, εs,1,a) = W s,1(Za) + εs,1,a (4)

= us − α(zw)ps(ι) + εs,1,a +∑e

E [W2(e, Za, ε2,a)] fe(e|Za).

The value of delaying the IVF decision until the start of the next period is:

Wd,1(Za, εd,1,a) = W d,1(Za) + εd,1,a (5)

= 0 + βE [W1(Za+1, ε1,a+1)] + εd,1,a.

Changes in Z across periods, in this case, are due to the patient becoming older, which affects her

fertility characteristics and the probability of a favorable outcome at any treatment stage. The

discounted expected value βE [W1(Za+1, ε1,a+1)] accounts for the expectation of ε, the payoffs in

W 1 associated with starting or delaying IVF at age a + 1, and patient’s option to choose the

optimal action. If the patient is already at age amax, however, she receives the terminal value

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WT (Zamax) = uT (zp) at the start of the next period and exits the model. This type of exit is also

possible in stages 2 and 4, described below, but we do not list it explicitly.

4.2 Stage 2: Continue vs. cancel

The patient makes her next significant choice after the value of e is realized. A larger value of e is

generally associated with a larger number of eggs (r) that are ready for retrieval from the patient’s

ovaries. During the second treatment stage, she considers e and her personal characteristics (Za)

while deciding whether to continue (c) or cancel (nc) treatment, thus Y2 = {nc, c}. If the patient

cancels treatment, she pays no additional treatment fees, and she is able to consider starting

treatment again in the future. If the patient continues treatment, she pays the additional fee pc,2(ι)

and undergoes a surgical process in which eggs are retrieved.

If the patient decides to stop treatment, she receives the value

Wnc,2(e, Za, εnc,2,a) = Wnc,2(Za) + εnc,2,a (6)

= 0 + βE [W1(Za+1, ε1,a+1)] + εnc,2,a.

The value of continuing treatment includes an expectation taken over values of r conditional on

the realized signal e and other patient characteristics:

Wc,2(e, Za, εc,2,a) = W c,2(e, Za) + εc,2,a (7)

= −α(zw)pc(ι) + εc,2,a +∑r

E [W3(r, Za, ε3,a)] fr(r|e, Za).

The full value of the second stage is the maximum of these two options.

4.3 Stage 3: Fertilization

If treatment is not cancelled, the patient’s eggs are retrieved and she observes the realized value of r.

The patient’s next choice is how to fertilize the eggs. The fertilization method is represented by the

variable m, and the patient’s options are: natural fertilization (m1) or with ICSI (m2). Thus Y3 =

{m1,m2}. The patient’s characteristics (Za), her number of eggs (r), and her fertilization choice

(m) determine the number of viable embryos generated for the patient. Couples with male factor

infertility (zmf = 1) are likely to receive the greatest benefits from fertilizing via ICSI (m = m2) .

When m = m2, the patient pays the additional price pm,3(ι).

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Let X represent a possible realization for the number of embryos. Possible values of X are in

{0, 1, 2, 3, 4+}. We cap the maximum value of X at 4 because this is the greatest number of embryos

that we see transferred to patients during the final treatment stage. When making her choice over

fertilization method, the patient considers the probability of receiving X embryos, fX(X|r,m,Za).

We write the patient’s choice-specific value from a third-stage action:

Wm,3(r, Za, εm,3,a) = Wm,3(r, Za) + εm,3,a (8)

= −α(zw)pm,3(ι) + εm,3,a +∑X

E [W4(X,Za)] fX(X|r,m,Za).

The patient selects the action, m, with the greater of two Wm,3(r, Za, εm,3,a) values.

4.4 Stage 4: Embryo transfer

At the start of the fourth and final treatment stage, the patient learns her number of viable

embryos, X. The patient chooses x, the number of embryos to transfer during the final treatment

stage, subject to x ≤ X. We assume that the patient selects x = 0 only if X = 0. A patient’s

treatment outcome is influenced by her number of embryos (x) and her personal characteristics

(Z). As a result of treatment, k children are born with probability fk(k|x, Za). Under current

policy, there is no price for this treatment stage. If treatment fails she moves to the start of the

next period, but if treatment is successful she waits for three additional periods (i.e. 9 months)

before making her next reproductive decision.

When the patient elects to transfer x embryos, she receives an expected benefit of

Wx,4(X,Za, εx,4,a) = W x,4(X,Za) + εx,4,a (9)

= η(x, Za) + εx,4,a + fk(0|x, Za)βE [W1(Za+1, ε1,a+1)]

+∑k>0

fk(k|x, Za){U(k|ka, τ) + β4E

[W1(Za+4, ε1,a+4)

]}.

This expression includes the possibilities of failed treatment (k = 0) and successful treatment

(k > 0). The future value of a patient’s decision, E [W1 (.)], depends on the realization of the

current treatment and the prices and policies that constrain the patient in future periods. If the

treatment is successful, Za evolves to a value Za+4 which reflects that the patient is one full year

older and has k additional children. Moreover, this future value is discounted at β4. If treatment

fails, then the next decision’s value is discounted by β, and Za+1 reflects that the patient is just

20

three months older. The value function captures the patient’s benefit from building a family of

a certain size during her fertile years, so statements about a patient’s desire to avoid the risk of

lifetime childlessness would be made in reference to W rather than U(k|k, τ).

4.5 Initiation decision

Now consider the decision of a potential patient at age a0 who is deciding whether to start IVF

for the very first time. This is somewhat different from the decision to begin a new cycle by an

already-active patient. We make the simplifying assumption that this potential patient does not

yet know her values of ZB, but she knows the population distribution of ZB values conditional on

age, fZB (ZBa0 |a0). The potential patient’s expected value from starting treatment is:

W(ZDa0)

= E[W s,1(Za0)|ZDa0

]=∑ZBa0

W s,1(ZDa0 , ZBa0)fZB (ZBa0 |a0),

where we make the distinction between the state variables known prior to treatment (ZDa0) and

those learned after treatment begins. The potential patient compares W(ZDa0)to the utility from

foregoing treatment, which we specify as WOUT (zr) = µ (zr) + ν. The parameter µ captures the

mean value of the outside option for potential patients of different races, and it is common across

potential patients of a given race. There is evidence that African-American women are less inclined

to pursue infertility treatment, and in our model this would be reflected in a higher value of µ. ν is

specific to each potential patient and captures heterogeneity in the value of permanently foregoing

IVF treatment; it explains why potential patients with the same ZDa0 and (unobserved) τ make

different choices with respect to ever pursuing IVF.25 One possible interpretation of ν is that of a

sunk utility cost that must be paid to pursue IVF. Some infertile women with strong objections

to IVF, e.g. because of religious beliefs, may refuse treatment even if it is free and has no chance

of failure. τ and ν play fundamentally different roles in the model. τ characterizes permanent

differences in utility from children. Potential patients know both their ν and τ before embarking

in IVF treatment. ν captures idiosyncratic preferences for taking the outside option relative to

pursuing IVF but plays no further role once the potential patient becomes a patient.26

Under these assumptions, the potential patient enters the clinic to initiate her first IVF cycle if

25Note that there is no ε1,s for this very first cycle.26 In a more general model, observationally similar patients, even with same τ and facing same ε, could make

different decisions, perhaps with those with high values of ν being more reluctant to use IVF multiple times thanthose with low values of ν. For computational tractability, though, we work with a simpler model in which once awoman decides to use IVF, heterogeneity in ν is no longer relevant for her decision-making within the clinic.

21

the expected value of pursuing IVF is greater than the value of foregoing treatment, and she exits

the model otherwise. We let the indicator I equal one whenever a potential patient initiates IVF

treatment, and equal zero otherwise. Then

I = 1⇔W(ZDa0)≥ µ (zr) + ν.

To make the decision problem more explicit in some of the analysis below, we sometimes add

the policy index g to our notation for the value of starting a patient’s first cycle, i.e W s,1 (Za0 , g).

We let g = gE represent the empirical baseline that we observe during the sample period. The index

g captures elements such as pricing, insurance, regulations, etc. Under alternative environments,

the value of W s,1 (and all other W y,j that follow) changes and therefore initiation decisions are

affected.

5 Data

5.1 Clinic data

Our primary data cover individual patient histories at the clinic during 2001-09. We observe all

treatment cycles conducted during this period for patients who underwent their first-ever IVF cycle

between 2001 and 2007, plus we observe cycles during 2001-09 for some patients who first received

IVF before 2001. While the data allow us to describe many patients’IVF histories from the start

of their treatments, we do not observe whether a patient returns to the clinic after 2009 or visits

a different clinic after her final visit at the clinic. We handle this potential right-censoring by

assuming that patients continue to make choices as described by our model, with no changes to the

policy environment, prices, or technology.

The main data sample contains treatment histories for 587 patients who use only fresh embryos

(i.e. not frozen), received their first-ever IVF cycle at the clinic between 2001 and 2007, and

have complete data on their personal characteristics and treatment details.27 We supplement

these observations with data from an additional 519 patients for whom we have data on all state

variables and most treatment choices. We refer to the expanded data as the “first-stage sample.”

The treatment histories contain information on 1,027 initiated cycles in the main sample and 2,176

in the full first-stage sample. Beyond the initiation decision and its Peak E2 score realization,

27 In practice, patients may choose to freeze excess embryos for potential later use, but we do not examine thatdecision. Frozen-embryo cycles account for only 12% of the clinic’s treatments during the sample period.

22

the main sample contains information on an additional 2,785 choices and stochastic health state

outcomes from stages 2-4 of IVF cycles. In the full first-stage sample we have complete data on

4,779 stage 2-4 choices and health outcomes.

In Table 2 we display some basic characteristics of the patients, their treatment choices, and

their outcomes; we separately report statistics for the main sample of 587 patients and the 1106

patients in the full first-stage sample. The average patient in the main sample is 34 years old at

the time of her first cycle in the clinic, and over half of all patients have insurance. Most insured

patients are from Illinois but not all; likewise most Illinois patients are insured but not all of them.

Most patients’homes are in a zip code with a median house price above $100,000, which we use

as a proxy for patient wealth (zw). We track race as a binary variable which indicates whether the

patient is African American (zr = 1) or not (zr = 0); 95% of patients have zr = 0. The patients in

the main sample have no children when they initiated treatment, but some patients in the first-stage

sample have prior children. The biological variables (ZB) exhibit some minor differences between

the main and first-stage samples, with the former set of patients displaying slightly worse fertility

characteristics.

At the bottom of Table 2 we display patient-level statistics on treatment choices and outcomes.

Patients in the main sample average 1.75 treatments during the sample period, and about half

experience at least one birth during their full treatment history. In Table 3 we report summary

statistics on choices and outcomes within treatment stages. Most patients at stage 2 choose to

continue treatment, with only a 14% cancellation rate. Most patients (60%) fertilize their eggs

with ICSI; this rate is closer to 90% when male-factor infertility is present.28 Finally, patients take

2.3 embryos on average during a treatment. The embryo transfer choices are most often made with

a choice set of 4+ embryos, due to over 6 embryos being generated during an average cycle. At

the bottom of Table 3 we report treatment-level outcomes. To obtain the main sample’s average

of 0.51 children born per cycle, we include all stage 4 decisions with x > 0 and birth outcomes in

{0, 1, 2, 3}. A singleton birth occurs in 27% of cycles, and twins occur in an additional 12%. While

we observe no triplet births in the main sample, they occur at a rate of about 1% in the larger

first-stage sample; this allows us to account for triplet risk when estimating the structural model.29

Some correlations among patient characteristics and treatment sequences suggest the role of

28While the options “full ICSI” and “partial ICSI” are separated in the data, we group them together in ourmodel.

29 In 2009, 1.6% of all U.S IVF births from fresh nondonor cycles were triplets or more. Conditional on 3 or moreembryos transferred, the triplet rate was 3.6% (Centers for Disease Control, 2014).

23

dynamics and the importance of the state variables in patients’decision-making. Almost 60% of

patients whose first cycle was unsuccessful returned for one or more additional cycles, while 16% of

patients with a first-cycle singleton and zero patients with first-cycle twins returned for additional

treatment. Patients who receive Peak E2 scores in the lowest quartile chose to cancel treatment in

40% of all cases, while patients with scores in the 25th − 75th percentile cancel only 4% of cycles.

Patients who are 35 or older take an average of 2.6 embryos in their first cycle, while younger

patients take 2 embryos on average. Uninsured patients take more embryos (2.4) during their first

cycle than insured patients (2.2), but this difference, which is statistically significant at the first

cycle, shrinks in the second and third cycle as insurance coverage is drawn down.

5.2 Market data

We use several pieces of market data to describe the set of potential patients for our clinic. These

data are used in a separate estimation step to estimate a model of treatment initiation. We assume

that potential patients are drawn from all zip codes with centroids within 75 miles of our clinic.

The area includes the city of St. Louis, its surrounding suburbs, and some rural towns outside

of the metro area. This area captures almost all of the patients who ever visit the clinic; a small

number come from greater distances.

We first describe the various data sources for the market data, and then we describe how they are

assembled into an estimate of the “at risk”population. We use the Centers for Disease Control and

Prevention’s (CDC) Vital Statistics database to construct the market’s distribution of maternal age

at first birth. This distribution, along with estimates of infertility rates by age from Dunson et al.

(2004), allows us to construct an age distribution for women who may consider IVF. We supplement

the Dunson et al. estimates with data from the National Survey of Family Growth (NSFG) to

estimate the difference in infertility rates by race. For zip code level information on the population

share with private IVF insurance, we use data from the 2012 American Community Survey (ACS)

and combine it with other sources of information, which we describe in the appendix. We collect zip

code level data on race and the median home values from the 2000 Decennial Population Census.

The home value data allows us to provide an estimate for the distribution of patients’wealth. We

combine the various zip code level data to construct an estimate of the joint distribution of wealth

IVF insurance coverage and our measure of wealth. Finally, we use data from the CDC on the

number of cycles conducted at each infertility clinic in the market to assess how many in the pool of

potential patients would rely on the clinic we study (rather than a different clinic), if they decided

24

to pursue IVF.

Next, we describe how we construct the pool of potential patients. Assuming stationarity and

stable cohort sizes, at any given point in time (quarter) there are N stl couples in the St. Louis

region who have optimal life cycle fertility plans that induce them to pursue their first pregnancy.

Therefore, in every quarter t there is a race-specific distribution of age at first (attempted) birth for

these women ft (a|zr) . Some of them will succeed immediately, while others will take more time. If,

after 12 months of natural attempts, the woman does not get pregnant, the couple is diagnosed with

clinical infertility. Let inf (a, zr) be an age- and race-specific infertility rate which increases with

age. Together,(N stl, ft (a|zr) , inf (a, zr)

)provide the number of women, N inf

a,zr , of each age and

race who realize that they are unable to conceive without IVF. These N inf =∑1

zr=0

∑amax

a=amin Ninfa,zr

women constitute the risk set, i.e. all women in the St. Louis region who may consider IVF

treatment. In a final step, we obtain the risk set for our clinic by deflating N inf to match the

clinic’s market share as reported by the CDC. In total across all years of the sample period, we

estimate that N inf = 2781 women consider treatment at the clinic we study. See Appendix B for

additional details on the calculation of N inf and its relationship to fZD(ZDa0), the distribution of

patient characteristics.

We compute race-specific empirical initiation shares, sinit (zr), for the clinic. We observe that

N clin = 828 new patients (including 35 African American) initiated treatment at the clinic during

the period 2001-2007.30 Using our estimates of N inf (zr), we calculate the share

sinit (zr) ≈N clin (zr)

N inf (zr)(10)

We find sinit (0) = 0.072 and sinit (1) = 0.346 which means that 7.2% of the clinic’s African Amer-

ican potential patients and 34.6% of its remaining potential patients decided to pursue treatment.

The remaining 1953 potential patients could be induced to seek IVF treatment through large enough

increases in W 1,s.

6 Empirical Specification

In this section we describe our assumptions regarding functional forms and how outcomes and

utility may vary with patients’observable characteristics.

30We use the 587 with complete data in estimation, but have records for 828 patients initiating treatment overthis period.

25

6.1 Treatment Technologies

During each treatment stage, a patient makes her choice while considering a probability distribution

over outcomes that will be realized at the stage’s conclusion. We now describe the functional forms

and data assumptions that describe the distributions.

In the first stage, a woman knows some basic facts about her fertility including ZB, and takes

drugs to stimulate egg production. We assume that the drug dosage is a function of the patient’s

age and her values of ZB. The woman’s characteristics and drug dosage affect a stochastic process

that determines her Peak E2 score, e. We model the probability of a particular e with a multinomial

logit model for fe(e|Za). In the data we observe e values between 0 and 10,196 pg/mL, with a mean

and median around 1,600, and 99% of all values below 4,500. In the empirical implementation, we

assume that the possible realizations of e are in discrete bins with values 0-500, 500-1000, 1000-

1500, 1500-2000, 2000-2500, and over 2500. We use a multinomial logit model here rather than an

ordered model because especially high values of e can be seen as bad for the patient.

In estimating fe, we include variables for a woman’s age, the average of any AFC scores she

receives over the entire treatment history, and her number of initially diagnosed fertility problems.

The age variables we include are indicators for whether the patient’s age is: 28, 29-31, 32-34, 35-37,

38-40, 41-43, or 44. (We exclude age 35-37 for the empirical implementation.) We separate the

patient’s AFC score (zafc) into categories for scores from 1-5, 6-10, 11-15, 16-25, and 26+, with

the highest category excluded for the empirical implementation. For patient fertility problems, we

include an indicator for whether the patient has one or more distinct diagnosed issues (zff = 1).

In the second stage, the patient observes her realized value of e and considers the number of

eggs, r, that might be retrieved if she continues treatment. The distribution of r depends on e and

Za. In the data, r takes integer values from 0 to 38 with a mean of 10.6 and median of 10. The

90th percentile is at r = 18, and 99% of all r values are below 27. We use an ordered probit model

for this distribution, with possible values of r as 0-4, 5-10, 11-20, and 21+. The variables that can

affect the realization of r are: indicators for possible values of e, split as they are in the model for

fe; the same age categories in fe; the AFC score categories from fe; and the indicator for whether

a patient has one or more documented fertility problems.

In the third stage, the patient observes her realized value of r and selects a fertilization method

(m). The patient’s number of transferable embryos, X, will depend on r, m, and the patient’s

characteristics. We model the process determining X with an ordered probit. We include as

26

regressors: the possible values of r as described in the model for fr; the patient’s age, AFC score,

and fertility problems as described above; and the patient’s choice of m plus the interaction of m

with an indicator for male-factor infertility.

In the final stage of treatment, the patient is subject to the stochastic process fk, which deter-

mines her number of live births. We model fk as a multinomial logit, with the probability of each

outcome determined by the number of transferred embryos, the patient’s age, and the indicator

for female fertility problems. Some patient and treatment characteristics, like AFC score or male

factor infertility, are not relevant here because their roles in determining outcomes is finished once

the patient has her set of transferable embryos.

6.2 Utility assumptions

We must make functional form assumptions for several expressions that are relevant for patients’

utility. In addition to the restriction that all patients have the payoff of U(k|k, τ) = 0 from zero-

birth outcomes, we assume that outcomes with k > 0 provide utility according to:

U(k|k, τ) = uk + κ× 1{k > 0}+ ζ × 1{τ = 2}

The parameter vector (u1, u2, u3) captures the lump-sum payoff from a singleton, twin, and triplet

birth to a patient with no prior children (k = 0). Given the health risks and other challenges

for triplets, we anticipate that u3 < u2 and u3 < u1, but these parameters are unrestricted in

estimation. The parameter κ captures any difference in the marginal benefit of a birth to patients

with prior children (k > 0); diminishing marginal utility from children would imply that κ is

negative. We account for the impact of ASRM guidelines on utility by specifying η(x, Za) =

η0 × 1{x, Za}, where η0 is a constant utility penalty and 1{x, Za} is an indicator function that is

equal to one for any choice of embryos (x) that is outside of the contemporary ASRM guidelines

for a patient with state variables Za.31

We assume a simple two-type structure for patients’ permanent unobserved heterogeneity.

A share of patients with type τ = 1 has preferences for birth outcomes represented only by

(u1, u2, u3, κ), while the remaining patients (with τ = 2) has, in addition, its utility payoff shifted

by a scalar parameter ζ. A patient’s probability of being of type τ = 2 depends on her state values

at the time she initiated treatment, ZDa0 . Along with a0, we allow the distribution of τ , conditional

31 In practice, no patients in the main data choose to go outside of the guidelines by more than a single embryo,so we do not have the opportunity to estimate different penalties for different degrees of violation.

27

on initiation, to depend on a measure of her wealth level (zw), her race (zr) , her initial number of

insurance-covered cycles (ιa0), and a dummy (zasrm0) for the ASRM guideline regime when treat-

ment started. The dependence of the distribution of τ on the state varaibles reflects the need to

acknowledge that differences across patients’ circumstances will result in a different selection of

patients depending upon their intensity of taste for children. The value of initiation depends on

various state variables and the unobserved type, and we expect a differential propensity to initiate

by the two types. For example, conditional on being uninsured, one would expect a higher preva-

lence of patients with high taste for children (relative to the prevalence among potential patients).

As a result, regardless of whether types are correlated with demographics in the pool of potential

patients, the distribution of types within the clinic will surely depend on the state variables. We

assume that the probability of a high type (τ = 2) is

Pr(τ = 2|ZDa0 , I = 1, ρ) =exp(ρ0 + ρ1a0 + ρ2zw + ρ3ιa0 + ρ4zasrm0 + ρ5zr)

1 + exp(ρ0 + ρ1a0 + ρ2zw + ρ3ι0 + ρ4zasrm0 + ρ5zr).

During estimation we restrict ρ0 < 0 for computational purposes, but this adds no real restrictions

on the utility parameters. For notational convenience, we let ρ represent a column vector of{ρj}5

j=0values. In addition, we write [1, ZDa0 ] as a vector containing 1 and an individual patient’s

row vector ZDa0 , and we let Λ represent the logistic distribution function so that Λ([1, ZDa0 ]ρ) =

Pr(τ = 2|ZDa0 , I = 1, ρ).

As the patient makes her choice between starting a treatment cycle or delaying, she considers

the additional flow benefit us which she receives (or sacrifices) when she begins a treatment cycle.

We assume that us = δ, a scalar parameter. The value of us is identified, in part, by the frequency

with which clinic patients return for additional treatment cycles following their first cycle.

The first three stages of IVF treatment include α(zw), the disutility from paying a price p for

some treatment component. We specify α(zw) as an affi ne function of zw: α(zw) = α0 + αwzw.

Since the effect of price is subtracted from within-stage value functions above, we expect α0 to

be positive for consistency with downward-sloping demand. If wealthier patients are less price

sensitive, this will be captured through αw < 0.

We assume that the terminal payoff uT is a function of the patient’s cumulative payments

for treatment. Children born due to treatment are not included here because those benefits are

included in U(k|k, τ). We add the variable zp as an indicator for whether a patient ever paid full

price for a treatment cycle. We assume uT = γpzp, which includes the normalization uT = 0 for

28

patients who have never paid the full price of treatment.

At the initiation stage we specify that the individual-specific taste shock ν is distributed ac-

cording to a continuous distribution F (ν) in the population of potential patients. The realizations

of ν are i.i.d. Moreover, we assume ν is independent of infertility problems and other observables in

our model, so F(ν| τ , ZDa0

)= F (ν) . We assume ν ∼ Logistic so we have F (ν) = Λ (ν) = exp(ν)

1+exp(ν) .

Let ϕ represent a vector of all of the parameters except µ, ζ, and ρ, and define θ = (ζ, ϕ, ρ).

We estimate µ separately from θ so it is convenient for us to distinguish between the two.

7 Estimation

We estimate the model in three stages. We estimate the treatment technologies, fe, fr, fX , and fk

in the first stage. These models are easy to estimate using conventional statistics packages. We use

the parameter estimates from this estimation step to characterize the stage-specific distributions

of treatment outcomes for each combination of fertility-related state variables and each possible

stage-specific action a patient may take. We implicitly assume that we, as econometricians, have the

same information on outcome probabilities as the patient and her doctor. Within this stage we also

estimate the distribution of fZB (ZB|a0) non-parametrically using frequencies of ZB realizations

from within the population of women who initiate treatment. In the second stage we estimate the

parameters in θ using data exclusively from the population of 587 patients who are observed within

the clinic. In the final stage, we estimate µ (zr) using our estimates of E[W s,1(Za0)|ZDa0

]together

with the market-level data.

7.1 Within-clinic Choices

Given the estimated treatment technologies, a guess at the value of the structural parameters

in (ζ, ϕ), and the distributional assumptions on ε, we are able to calculate W y,j(Za, τ ; ζ, ϕ) and

E [Wj(Za, τ ; ζ, ϕ)] for each y and j at every Za. We perform this calculation by backward recursion

separately for each type τ . For each potential state that might be reached when the patient is

age amax, we use (ζ, ϕ) to compute the terminal payoff, the values of W y,j(Zamax , τ ; ζ, ϕ) working

backwards through treatment stages, and the logit inclusive value E [Wj(Zamax , τ ; ζ, ϕ)] for each

stage. We then move to age amax − 1 and use the amax expected utility values while constructing

W y,j(Zamax−1, τ ; ζ, ϕ) and E [Wj(Zamax−1, τ ; ζ, ϕ)]. The procedure continues back to age amin.

Let dy,j,a,i ∈ {0, 1} represent patient i’s binary choice whether to take action y in stage j while

29

at age a. We write di as the patient’s complete history of choices at the clinic. We use the calculated

values ofW y,j(Za, τ ; ζ, ϕ) for all Za and τ to compute choice probabilities for each observed decision

in our data. Conditional on a patient’s type τ , calculating this probability is a straightforward task

due the i.i.d. extreme value assumption for the ε terms. For example, conditional on a patient

reaching a stage 2 decision over whether to continue (c) or cancel (nc) the current treatment cycle,

her probability of continuing is:

Pr(dc,2,a,i = 1|Za, τ ; ζ, ϕ) =exp[W c,2(Za, τ ; ζ, ϕ)]

exp[W c,2(Za, τ ; ζ, ϕ) +Wnc,2(Za, τ ; ζ, ϕ)](11)

The values of W c,2(Za, τ ; ζ, ϕ) and Wnc,2(Za, τ ; ζ, ϕ) are relatively simple functions of the esti-

mated treatment technology fr, price and its disutility parameter, and the calculated values of

E [W3(r, Za, ε3,a)] and E [W1(Za+1, ε1,a+1)] . We calculate a probability like this one for each ob-

served decision by each patient, including the implicit choices to delay further treatment attempts

which occur during periods when the patient does not appear in the data despite starting treatment

during some earlier period.

A patient’s permanent unobserved type, τ , affects every period and stage of her decision prob-

lem. Let Pr(dy,j,a,i = 1;Za, τ , ζ, ϕ) represent the predicted probability that patient i takes the

observed action dy,j,a,i if she has type τ . The patient is observed starting in period ti,0 and ending

in Ti. Conditional on ζ and ϕ, the type-specific joint probability of observing patient i’s sequence

of choices is:

Li(di; τ , ζ, ϕ) =

Ti∏a=ai,0

4∏j=1

Yj∏y=1

Pr(dy,j,a,i = 1;Za, τ , ζ, ϕ)dy,j,a,i .

With i’s true type τ unobserved, the likelihood of observing her choices requires integration over

τ , which is simply

Li(di; θ) =∑

τ Li(di; τ , ζ, ϕ)fτ (τ |Zi,a0 , I = 1, ρ).

The log-likelihood of observing the choices of all patients in the clinic data is

L(θ) =∑i

log[Li(di; θ)].

We estimate θ by maximizing the value of L(θ). We compute standard errors following the “outer

product of the score” method for θ only. In computing standard errors we do not account for

potential sampling error in our first stage estimates.

30

In this second stage, the key model parameters recovered by the maximum likelihood procedure

are the “price coeffi cient” (α0) and the non-parametric utility from children, given by uk for k =

1, 2, 3. Identification of α0 comes from various features of the clinic data. Specifically, it primarily

draws on the following three sources of variation. First, since every patient that we observe at the

clinic started at least one cycle, cross-sectional differences in insurance coverage during the first

cycle provide identifying variation through different cancellation decisions. Greater price sensitivity

induces patients facing higher prices (due to insurance variation) to be more selective in their

decision to continue on to the second stage — the most expensive one — involving egg retrieval.

Second, while all clinic patients started at least one cycle, uninsured patients are (all else equal) less

likely to return for another attempt after an initial failure. Again, the greater the price sensitivity

measured by α0, the greater the observed differential return rate of uninsured vs. insured patients.

Third, additional variation comes from the observed behavior of the subsample of initially-insured

patients as they approach the exhaustion of their covered cycles, relative to their behavior in earlier

cycles. The greater the price sensitivity, the greater the tendency of insured patients to take actions

that either preserve the last remaining insured cycles (by cancelling more often) or make sure that

the cycle succeeds (by increasing the number of embryos transferred). Identification of αw comes

from contrasting these arguments in subsamples of low versus high wealth patients.

The identification of the uk values can be obtained with the embryo-transfer choice data under

our assumption that patients know the probabilities of different birth outcomes for each potential

embryo choice. Through her embryo-transfer choice, the patient essentially chooses among different

potential lotteries over birth outcomes k. For example, if patients strongly dislike triplet outcomes

(i.e. they have a very negative value for u3), then they will avoid embryo choices that are more

likely to produce triplets. While the identification of the uks does not require variation in ASRM

guidelines, which changed in the middle of our sample period (2004), such variation is also helpful

for identification. Comparing the transfer behavior of patients with similar characteristics facing

different recommended choice sets helps identify preferences for birth outcomes as well as the

penalty parameter η0. Of particular value is data on how similar patients behave when guidelines

change with respect to single embryo transfers.

31

7.2 Treatment Initiation

We estimate the initiation decision in a third step, taking the within-clinic estimates from the

second step θ = (ζ, ρ, ϕ) as given. Under our assumptions about initiation, we may write

Pr(I = 1|ZDa0 , τ , ϕ, ζ, gE , µ

)= Λ

(W(ZDa0 , τ , gE , ϕ, ζ

)− µ (zr)

), (12)

where the variable I indicates whether a patient with characteristics ZDa0 started treatment at

age a0. We integrate over observed and unobserved patient characteristics to compute the model

predicted rates at which the clinic’s potential patients of both races actually become patients,

sinit(µ (zr) ; gE , θ

). These race-specific distributions —fZD|zr(Z

Da0) for observed characteristics and

fτ |zr(τ |ZDa0) for unobserved heterogeneity —will in general be different in the full potential patient

pool versus among patients who choose to initiate treatment. We estimate the parameters µ (zr)

by solving

sinit(µ (zr) ; gE , θ

)= sinit (zr)

for each race zr under the empirical policy setting, gE . sinit (zr) is the race-specific, empirical

initiation share that we construct from the count of actual patients given zr and our estimate of

the size of the potential patient pool with race zr. sinit is the initiation share predicted by the

model for a given value of µ(zr). We estimate µ for each race by finding the value that makes the

model-predicted race-specific initiation share sinit match the observed share, sinit. Note that under

alternative policies, W(ZDa0 , τ , g, ϕ, ζ

)will change but µ (zr) remains fixed.

We approach the distributions fτ |zr(τ |ZDa0) and fZD|zr(ZDa0) using different strategies. In Ap-

pendix A we show that our assumptions on: a) the distribution of unobserved types conditional

on treatment initiation, fτ(τ |ZDa0 , Ii = 1, ρ

); and b) the initiation decision, are suffi cient to back-

out the unconditional (on initiation) race-specific distributions fτ |zr(τ |ZDa0).We write the incidence

of τ = 2 within-clinic as Λ([1, ZDa0 ]ρ), and Λ(W(ZDa0 , τ , gE , ϕ

)− µ (zr)

)provides the race-specific

probability of initiation for τ = 1, 2. In Appendix B we describe our approach to constructing

fZD(ZDa0) using market data.

The estimates for fτ |zr(τ |ZDa0

)and fZD|zr

(ZDa0)allow us to derive sinit (θ, µ (zr) , gE) , the

model-predicted fraction of potential patients of race zr who actually become patients). To ob-

tain sinit (µ (zr) ; gE , θ) , we integrate the initiation probability Pr(I = 1|ZDa0 , θ, τ , µ (zr)

)over the

32

race-specific distribution of ZDa0 and τ among potential patients

sinit(µ (zr) ; gE , θ

)= Pr

(I = 1|θ, µ (zr) , gE

)=∑

ZDa0

[∑τ

Λ(W(ZDa0 , τ , gE , ϕ, ζ

)− µ (zr)

)fτ |zr

(τ |ZDa0 , µ, θ

)]fZD|zr

(ZDa0)

We use a bootstrap procedure based on the sampling distribution of θ, to construct a confidence

interval on µ for each race. In particular, we draw 400 times from θ’s distribution, and for each draw

we calculate the values of µ that equate sinit and sinit for each race. We then sort the individual

estimates of µ and use the 2.5th and 97.5th percentile values as the 95% confidence interval. The

confidence interval on µ is not interesting in own right, but it plays a critical role in describing the

precision of predicted treatment-initiation decisions, which we discuss below.

8 Results

8.1 Technology estimates

In this subsection we discuss our estimates of the four treatment stages’ technologies. These

technologies are dependent on a patient’s characteristics, and a patient’s knowledge of them is a

crucial part of how she solves her personal dynamic optimization problem. Rather than providing

parameter estimates for each treatment technology, we use a collection of figures to discuss the role

each technology plays in the choice process. One of our overall goals is to emphasize the importance

of allowing forward-looking dynamic behavior at each treatment stage.

During the first treatment stage, the patient decides whether to start or delay an IVF cycle.

She is aware of her full state vector, Z, which includes her AFC score, zafc. At this point in the

decision process, she considers her probable peak estradiol score (e), which will be revealed in Stage

2 if she starts treatment. In Figure 2 we display (estimated) probability distributions over e for

two AFC score categories. The figure shows that having an AFC score below 5 substantially shifts

to the left the distribution of e that the patient can expect to realize at the beginning of stage 2.

The patient cares about her value of e because it affects outcomes in later stages. In Figure 3 we

show that the realized e influences the distribution of the number of eggs that will be successfully

retrieved (r) in stage 3. Indeed, if e is low (e.g. in the 500-1000 range) the mode of the distribution

of eggs is 6-10 whereas if e is relatively high (2000-2500) the mode of the distribution of eggs is 11-20

33

and the probabilty of a low egg count (1-5) is almost zero. This strong difference in r outcomes at

different values of e justifies our treatment of e as a within-period state variable that is critical to

continuation/cancellation decisions in stage 2.

In treatment stage 3, a patient chooses her fertilization method (m). This choice, interacted

with the patient’s state variables, influences the distribution of available embryos (X) in stage 4.

In Figure 4 we display the distributions of X with (m2) and without (m1) ICSI for patients whose

partners have male-factor infertility. The figure shows that the more technologically advanced

fertilization method (ICSI) shifts the distribution to the right, increasing the probability of having

4 or more viable embryos and reducing the probability of having a small embryo count.

Once the patient has realized her value of X, she chooses the number of embryos (x) to transfer

back into the uterus subject to x ≤ X. In Figure 5 we display evidence on how x affects the

distribution of births (k). Transferring 3 embryos instead of 2 reduces the chance of no birth from

about 60% to under 50%, but the probabilities of twins and triplets increase. It is important to

notice, however, that the probability of having no live births is fairly high regardless of whether

2 or 3 embryos are transferred. Finally, in Figure 6 we explore the effects of age. We focus on

patients who transfer x = 3 embryos in stage 4. As expected, the distribution for older (age > 35)

women shifts to the left, noticeably increasing the odds of no live birth.

8.2 Utility parameters

Taking as inputs the technology parameters described above, we estimate the model’s structural

taste parameters. In Table 4 we display our estimates of U(k|k, τ), α, δ, γ, and η. Our estimates

of u1, u2, and u3 represent payoffs from different birth outcomes to patients with τ = 1 and no

prior children. These estimates show that patients receive a positive payoff from a singleton or twin

birth, with the latter valued slightly more. Triplet births, by contrast, have a negative utility payoff

for patients. The estimate of κ indicates that patients with 1 or 2 prior children have their utility

from births shifted downward substantially. For example, for a patient with k > 0 and τ = 1,

the estimated κ implies that the patient would prefer no additional children. The taste shifter ζ

associated with type 2, however, is suffi cient to increase the utility from additional births to be

positive for patients with k > 0.

Table 4’s results indicate that the baseline price disutility is significantly different from zero

for all patients, and this disutility is smaller for high-wealth patients. We recover a significantly

negative estimate for the start/delay parameter δ, which plays a large role in determining whether a

34

patient returns for additional treatment cycles after her first. Our estimate of the parameter γ, for

a patient’s terminal payoff uT , shows no significant difference between the utility of patients who

have paid out-of-pocket for a treatment and those who have not. The final utility parameter on

Table 4 is η0, the utility shifter from selecting an x outside of ASRM embryo transfer guidelines. We

recover a negative value for this parameter, indicating a penalty for deviating from the guidelines.

Table 5 reports results on the distribution of τ within the treated population. We estimate

that about half of the patient population has type τ = 2 given their Z values. To interpret the

individual ρ parameters, consider the case of patient wealth. The negative coeffi cient (ρ2) on the

wealth measure indicates that a high-wealth person selected from the treated population is less

likely to have type τ = 2 than a treated low-wealth person. This accords with the intuition that

treatment expenses are most likely to discourage low-wealth individuals with relatively small payoffs

from having children through IVF.

Finally, in the third estimation step we recover µ(1) = −0.34 for African Americans and µ(0) =

−2.17 for all other potential patients.32 These values of µ ensure that the initiation model generates

treatment initiation decisions such that, as estimated from our data, 30% of all potential clinic

patients (7.2% of African Americans and 34.6% of others) indeed choose to become clinic patients

and undergo at least one IVF cycle.

8.3 Model fit

We conduct two procedures to evaluate model fit. First, we compare the estimated model’s pre-

dicted choice probabilities to those we observe in the data. This provides a straightforward way

to examine choice probabilities at the four stages of IVF treatment; all predictions match the data

fairly well. Start/delay decisions, which are observed most frequently in the data (and are assisted

by the intercept term δ) have the tightest fit. In all periods after initiation, patients in the data

choose “start”in 3.9% of all opportunities, while our estimated model predicts that patients choose

“start”with frequency of 3.5%. Stage 2 and 3 predicted decisions also follow the data fairly closely.

Some differences are to be expected, however, because these stages’fits depend on overallWj values

rather than individual parameters. We observe cancelation (stage 2) and ICSI (stage 3) frequencies

of 15.0% and 42.7%, respectively, and our model provides choice probabilities of 21.9% and 57.3%.

Figure 7 provides a comparison of distributions across stage 4 choices. The estimated model suc-

ceeds in matching x = 2 as the most common choice in stage 4, followed by x = 3. Transfers of 1

32The 95% confidence interval for µ(1) is [−0.85, 0.50] and for µ(0) is [−2.57,−1.57]

35

and 4 embryos are rare in the data (and model) because of the utility penalty for deviating from

ASRM guidelines and the negative payoff from a triplet birth (in the case of x = 4).33

In a second set of exercises, we evaluate the predicted choice and outcome histories for the

population of 587 observed patients. These histories begin with the same state variables (Z) as

the patients in the data, but then random draws on medical outcomes and taste shocks determine

choices and outcomes over time. For each patient we repeat the process ten times, allowing for the

realization of different taste shocks and stochastic medical outcomes. We average over patients and

their individual simulated histories in computing the statistics we report below.

We focus on two critical measures of effectiveness and effi ciency of IVF treatment. First we ask:

What proportion of patients eventually succeed in delivering at least one live birth through IVF,

regardless of the number of attempted cycles required to do so? We find that 59% of our simulated

patient histories include a birth, which is reasonably close to the empirical value of 53% reported

on Table 2. Second, we investigate how many cycles an individual patient receives at the clinic. In

our simulation, 53% of patients are observed taking a single cycle, 28% undergo two cycles, and

19% receive three or more cycles. These results compare very well to the data, in which we see

54%, 27%, and 19% of patients receive one, two, or three or more cycles, respectively. Patients’

responses to price variation, which come through differences in insurance status, also match well

between the data and model. In the data, insured patients take an average of 1.97 cycles during

their full treatment histories, while uninsured patients average 1.50 cycles. Our simulated patient

histories contain an average of 1.99 cycles for insured patients and 1.56 for uninsured. Both the

data and simulated histories contain only small differences in embryos transferred by insurance

status; we return to the relationship between insurance and embryos below.

9 Counterfactual experiments

We use the estimated model to consider a set of counterfactual policy experiments which analyze

potential IVF patients’responses to changes in their decision environment (g). The policies vary in

how they emphasize or highlight the key incentives and tradeoffs in IVF. Three themes are central

to all policies. First, with forward-looking patients, the full sequence of treatment choices can be

affected by prices and restrictions at any point on the treatment path. This is especially important

33We have explored whether choices in a patient’s second IVF cycle or beyond can be explained by outcomesduring stage 1-3 of her first IVF cycle. These variables have no significant impact on later-cycle choices. We viewthis result as evidence to support our assumption that the patient does not respond to health variables other thanthose in ZB or revealed during the current cycle.

36

for prices or opportunities that might change several periods into the future, like the exhaustion

of covered cycles under treatment-based insurance. Second, patients have a general incentive to be

aggressive in treatment because they do not face the full costs of high-order births. Third, patients

may have an incentive to take aggressive treatment in the current period in order to reduce the

probability of paying for treatment in the future.

Extensive-margin choices are crucial for this analysis, so we employ the full at risk population

of N inf = 2781 potential patients described above. While we abstract-away from the impact of IVF

policy on women’s lifecycle choices over education, career, age at marriage, and age at first birth,

these channels could affect the size and composition of the IVF patient pool.34 The N inf potential

patients represent the portion of St. Louis market served by the clinic we study. While we do not

discuss other clinics in the market, in our counterfactuals we implicitly assume that all clinics are

subject to the same policies. When considering absolute magnitudes below (e.g., numbers of births,

dollar values) these figures can be multiplied by about three to understand the impact of a policy

on outcomes in the St. Louis market as a whole. In 2012, St. Louis clinics performed about 1% of

all cycles in U.S. clinics.

For each potential patient, we draw age, wealth, insurance, race, and ASRM regime values

that are consistent with the empirical distributions of these values. Along with the distribution

of biological state variables (not yet revealed to potential patients), we use the estimated model

to construct W(ZDa0 , τ , g, ϕ, ζ

)for each simulated woman. The values of W

(ZDa0 , τ , g, ϕ, ζ

)differ

across policy experiments. We then allow potential patients to elect whether to begin treatment

by comparing W(ZDa0 , τ , g, ϕ, ζ

)to the population-wide utility parameters µ(zr) and a simulated

value for the potential patient’s taste shock ν. For all potential patients, we simulate initiation

choices and decision histories in the same way described above for evaluating model fit, including

repeating the process ten times for each potential patient in N inf . Potential patients who do not

start treatment at a0 exit the model forever.

We assume that the N inf simulated potential patients arrive at the fertility decision uniformly

over the 2001-07 window during which the 587 observed clinic patients began treatment. As in the

data used for estimation, the simulated patients’histories are followed from their initiation decision

through 2009. To maintain consistency with our empirical model, we focus on counterfactual

outcomes during 2001-09, and we continue to refer to this window as the “sample period.”

34Buckles (2005), Abramowitz (2014) and Gershoni and Low (2015) consider the impact of IVF policy on lifecyclechoices. If these choices change with the counterfactual policies that we consider below, then our estimates of welfareimpacts would change as well. We defer this issue to future research.

37

Across all experiments we hold fixed the clinic’s prices. While substantial changes in the policy

environment may prompt the clinic to adjust its prices, we do not offer a model of how new

equilibrium prices would be set. The clinic is part of a large medical school’s teaching hospital, so

it is not clear what objective function is used to set prices. We note that during the full sample

period the clinic elected to keep its prices fixed at the same level. In fact, the typical IVF cycle

price in the U.S. has remained approximately unchanged between the mid-1990s and the present,

despite a substantial increase in the number of treated patients.

We report our main results in Tables 6-7 and Figures 8-9. The tables contain both point esti-

mates of counterfactual outcomes and 95% confidence intervals calculated with the same bootstrap

procedure described above.35 The figures focus on embryo transfer choices and birth outcomes

under selected policies in which these choices and outcomes are particularly interesting. Because

the figures and tables contain results from all experiments collected together, it is worthwhile to

introduce them briefly and define terms. First, we calculate histories for N inf potential patients

under the observed choice environment; we refer to this as the “Empirical baseline”and index it as

gE . We then consider a variety of insurance policies that provide patients with a specified number

of treatments. We begin by simulating the market when no patients have treatment insurance (“No

insurance,”gN ). We contrast this with a policy that provides Illinois-style insurance for four IVF

cycles to all potential patients, without exceptions, in both states; this is “Universal insurance for

treatment”and is indexed as gIT . We augment gIT with three policies designed to reduce embryo

transfers. An “IT + embryo cap” (gC) policy limits all patients to transferring a single embryo.

The policy “IT + actuarially fair top-up prices”(gAT ) allows patients to receive multiple embryos,

but they bear the entire additional expected birth costs from multiple-embryo transfers. In the

final experiment with treatment-focused insurance, we illustrate the implications of reduced but

positive top-up prices (“IT + moderate top-up prices,” gMT ). We contrast treatment-focused in-

surance with outcome-focused insurance in two final policy simulations. First, we allow patients to

receive as many insured treatments as they choose, provided they have one or fewer children when

each cycle begins (“Universal insurance for outcomes,”gIO). Second, we demonstrate the impact

of dynamics and forward-looking behavior by simulating the impact of an outcome-based insur-

ance policy in which insurance benefits are reduced for older patients (“Age-adjusted insurance for

35We draw 400 times from the sampling distribution of θ, and then estimate a new value of µ for each draw. Weuse each pair (θ, µ) to compute the full set of patient histories under each counterfactual policy described below.We construct confidence intervals using the 2.5th and 97.5th percentile of each outcome (across (θ, µ) pairs) within apolicy setting.

38

outcomes,”gIA).

Before describing the individual policy experiments, we describe some of the outcomes that

we calculate under the empirical distribution of insurance (gE). Under the observed prices and

constraints, we find that 29.9% of potential patients elect to begin treatment. This initiation rate,

combined with success probabilities within the clinic, results in 15.9% of women in N inf achieving

at least one birth during the sample period. About 53% of simulated patients who begin IVF

achieve a birth at some point in the treatment history; this matches the observed rate in the actual

patient population. On average across ten simulated histories under gE , the baseline simulations

average 456 births for the 2781 patients in N inf ; these births deliver 636 infants to the population,

implying an average number of infants per birth of 1.4.

For each patient who begins treatment we calculate ∆i = W(ZDi,a0 , τ i, g, ϕ, ζ

)− (µ (zr) + νi),

which is a measure of the net utility gain from initiating IVF above the outside option. Patients who

elect to forego treatment receive ∆i = 0. We use αi, our estimate of the disutility from payments

for each patient i (which varies depending on i’s wealth) to obtain a patient-specific dollar-valued

surplus measure, CSi(g) = ∆i/αi. Across all potential patients in N inf , including those who do not

initiate treatment, the total CS(gE) = $10.3M, or about $3,700 per person in the risk population (or

$12,400 conditional on initiation).36 If insurers must pay the difference between insured patients’

prices and the full price, the empirical baseline requires a total of $3.6 million in payments from

insurers to the clinic. Finally, we calculate the total medical costs of all pregnancies and births that

occur under gE , using the cost estimates from Lemos et al. (2013) discussed above.37 Using these

figures, the total pregnancy- and delivery-related medical cost of the baseline is $31.4 million, or

$68,900 per birth. When insurance costs for treatment are included along with delivery costs, the

average cost per birth is $76,872 (or $55,105 per child).

We use the simulated population to calculate price elasticities as well. Prices paid by insured and

uninsured patients have different interpretations, so we calculate changes separately with respect

to each price. When out-of-pocket prices for uninsured patients rise by 5%, we calculate that 6.4%

fewer uninsured patients initiate treatment, implying an elasticity of −1.28 at the extensive margin.

36Policies that have increased insurance costs (e.g. from universal insurance) will eventually pass these costs onto consumers in the form of higher premiums, and this could reduce welfare. Two factors, however, may moderatethis welfare loss. First, the population of individuals purchasing health insurance policies is much larger that the riskpopulation we focus on, so per-capita premium increases could be small Second, insurance coverage of IVF wouldprovide additional benefits to women who do not know whether they will join the risk pool. These issues are beyondthe scope of our paper.

37We were unable to obtain actual cost data for individuals in our sample since deliveries may occur at any hospitalchosen by the patient. Data from the National Inpatient Sample shows that delivery costs in Missouri are similar tothose nationwide, while Illinois is slightly above the national average.

39

The same price increase has a slightly larger impact on the total number of uninsured cycles, which

falls by 6.7% for an elasticity of −1.33. The elasticities values are different, in part, because patients

who continue to initiate despite higher prices may choose to reduce their total numbers of cycles.

We perform the same calculations with prices paid by insured patients (holding fixed uninsured

prices), and we obtain elasticities that are smaller in magnitude. The impact of a 5% increase in

out-of-pocket expenses for insured patients results in 1% fewer insured patients initiating and a

total reduction of 1.4% in insured cycles. While elasticities above −1 are inconsistent with profit

maximization, the clinic may have different objectives than a traditional firm. These elasticities

are comparable to others from the health care literature (e.g., Manning et al., 1987).

9.1 Impact of insured treatment

In our first set of counterfactual policies, we consider the impact of a substantial expansion of

insurance in the market. To establish a baseline, we begin by simulating treatment choices and

outcomes when no patients have insurance (gN ). In this setting, we find that 24.2% of the at-risk

population chooses to initiate IVF, and 12.7% of the at-risk population conclude treatment with

one or more births. The availability of IVF generates $7.6M in surplus for patients, who initiate

treatment only if expected surplus is positive. While there are no insurance costs of treatment in

this setting, patients who become pregnant and give birth generate $25M in medical costs, which

amount to $69,414 per birth.

When Illinois-style insurance is extended to all potential patients (gIT ), the number of treated

women and births increase substantially. We find that 57.7% of potential patients in the simulated

risk pool initiate treatment, and 31.5% in this population experience a birth during the sample

period.38 The presence of insurance has an impact on both initiation and the choice whether to

continue treatment after a failure. While patients without insurance (in gN ) take an average of 1.24

cycles over their treatment histories, insured patients receive 1.43 IVF cycles on average. Despite a

reduction in the price of treatment, the distribution of embryos transferred is very similar under gN

and gIT (Figure 8). Likewise, the distribution of births (Figure 9), shows little difference between

gN and gIT . This suggests that the extension of insurance benefits has a minimal impact on the

38 If, contrary to our assumptions, potential patients have some information about ZB prior to initiating treatment,we expect that this could affect the magnitudes of our policy predictions. For example, if prior information aboutZB implies that patients who select into treatment have better fertility characteristics than the average woman whoexperiences infertility, then policy changes which reduce IVF’s price would have a smaller impact than we predict.On the other hand, if patients choose how quickly to move from lower-tech infertility treatments to IVF, then aprice-reducing policy change might result in relatively more new patients with favorable fertility characteristics.

40

multiple birth rate, whether through patient selection or the incentives of patients who would have

received treatment when paying full price. In our model, this is explained by the strong utility

benefits that patients receive from twins, and the relatively low risk of triplets. Taken together,

patients have little reason to reduce the aggressiveness of their embryo-transfer decisions.39

The patient surplus benefits of Illinois-style insurance are substantial, with total CS(gIT ) =

$18.4M, which is $10.8M greater than under gN . To evaluate the full impact of gIT , however, we

must account for additional costs due to insurance payments and medical delivery costs. As reported

on Table 7, the insurance costs of gIT are substantial, at $16.4M. The difference between the changes

in consumer surplus and insurance costs is to be expected considering the traditional medical-

demand “moral hazard” incentive of patients to take insured treatment when their willingness to

pay is less than the price for uninsured patients. The expansion of insurance coverage, therefore,

must be defended through arguments about fairness or equal access. While all potential patients

benefit from universal insurance, we find in supplemental analysis that increases in access and

surplus are greater for patients from lower wealth areas (zw = 0). Overall insurance and delivery

costs per birth are $85,213 with policy gIT , although the difference between this figure and the

no-insurance value is almost entirely due to the introduction of insured treatment costs. Delivery

costs per birth are largely unchanged because the distribution of birth outcomes is unchanged.

9.1.1 Embryo caps

We next explore the impact of restricting patients to transfer only a single embryo during treatment.

We do this in the context of universal insurance so that our setting is close to the implementation

of embryo caps as they have been introduced in practice, i.e. in countries with generous health

insurance. To simulate the policy gC , we solve the model again at the estimated parameters but

we impose the restriction x ≤ 1 instead of x ≤ X in stage 4 (the embryo transfer stage). We also

remove the utility penalty for single-embryo transfers for circumstances when these conflict with

ASRM guidelines. We then use the new policy functions together with the same history of ε and

medical technology shocks to simulate counterfactual patient histories under the one-embryo cap.

The restriction on embryo transfers reduces the expected value of IVF for patients considering

treatment. The share of N inf who initiate is 28.7%, or about half the initiation rate with gIT . The

cap has a large mechanical effect on the distribution of embryos transferred (see Figure 8), which in

39By contrast, Hamilton and McManus (2011) find that insurance mandates reduce embryo transfers. That result,however, is based on an earlier sample period (1995-2003) when IVF technology was more likely to fail and patientstransferred an average of one additional embryo per treatment.

41

turn yields a substantial shift in the distribution of births (Figure 9). As a consequence, the share

of patients with births (7.7%) declines more steeply than the initiation rate. The estimated stage

4 function fk(k|x, Z) implies a fairly high twin rate among single-embryo transfers at the clinic, so

the number of delivered infants is 1.14 for every birth despite the single-embryo restriction.

Despite an initiation rate that is greater than that of gN , the embryo cap policy generates less

consumer surplus ($5.6M) than the no-insurance scenario. Total insurance and delivery costs are

substantially reduced in magnitude, to $7.3M and $8.4M respectively, but important differences

exist between measures of costs per birth. Medical costs per birth fall by almost $30,000 relative to

gN and gIT , down to $38,900, due to the reduction in the numbers of twins and triplets. Patients

require more IVF cycles to achieve a birth, however, so insurance expenses along with medical costs

results in total per-birth costs equal to $72,400, which is greater than the average in gN .

9.1.2 Top-up prices

Patients receive substantial value from the opportunity to transfer two or more embryos, which

suggests that there may exist beneficial policies that allow patients to trade-off between the benefits

and costs associated with transferring multiple embryos. The medical cost of multiple births are

largely borne by insurers rather than the patients who choose treatment aggressiveness, which

implies a traditional form of moral hazard (distinct from the demand-related version associated

with gIT ) in which too much risky behavior occurs in equilibrium.

We construct top-up prices that are paid when a patient transfers two or more embryos. Let ck

be the average medical cost of a delivering k infants, and let Z denote the state variable values for a

median-age treated patient with no additional fertility problems. We construct an (approximately)

actuarially fair top-up price for transferring x > 1 embryos as:

px,4 =∑k>1

(ck − c1)[fk(k|x, Z)− fk(k|1, Z)].

This expression acknowledges that there is some multiple birth risk for patients transferring a single

embryo, fk(k|1, Z), but patients do not pay for this risk as part of the top-up price. Additionally, by

including the cost difference (ck−c1) we exclude the expense of a singleton infant. Given the values

of ck provided above (roughly $27,000, $115,000, and $435,000 for singletons, twins, and triplets,

respectively) and the probabilities in fk, the top-up price for two embryos is about $12,000, and

42

three or four embryos each entail top-up prices of roughly $19,000.40 In our simulations, when a

patient chooses to pay px,4 > 0, we subtract this price from the summed medical costs of the full

population’s treatment (as if the accumulated top-up prices are saved in a fund to pay for medical

expenses.) In calculating patient utility from any x, we remove the utility penalty (η0) for any

transfer outside of ASRM guidelines.

This top-up price policy (gAT ) generates greater total consumer surplus ($7.8M) than gN or gC ,

which leads to an IVF initiation rate that is greater as well. In addition, despite positive insurance

cost of $8.3M under gAT , the medical cost of births decreases by $13.1M relative to gN . Together,

these results imply that a policy of insured treatment for all patients, but with actuarially fair

top-up prices, is welfare-improving for both consumers and the insurance firms that pay for IVF

and birth costs. Reduced total costs for insurers could lead to lower premiums for patients in a

competitive insurance market. The policy gAT has a slightly lower share of potential patients with

a birth than gN (11.3% vs. 12.7%), but this is accompanied by a multiple-birth rate that declines

substantially. The average number of infants per delivery is 1.24 under gAT , which is about halfway

between the rates of gN and gC . The total cost per birth falls to $63,350 with gN , which is the

lowest value of all policies we consider in this paper. While both gC and gAT have per-birth medical

costs of about $37,000, the greater per-treatment success rate of gAT drives total per-birth costs

below those of gC .

While gAT has several attractive properties relative to gN and gC , the actuarially fair top-up

prices can lead some patients to pay total prices that are substantially greater than under gN . It

is possible scale-down gAT’s top-up prices to achieve a variety of policy objectives. For example,

the top-up prices could be set so that total consumer surplus is equal to the empirical status quo,

or they could be set so that total IVF and medical costs with top-up prices are equal to their level

under gN . We conclude our consideration of top-up prices with an additional example: prices that

prevent any patient from paying a greater price for an IVF cycle than she would under gN . We

scale-down the actuarially fair prices (while keeping their proportions fixed) so that patients pay

$5,000 to transfer a second embryo and $8,000 for three or four embryos. These payments are on

top of the insured treatment prices, which total $3,000 for a full cycle with ICSI. Under gN a patient

who uses ICSI and receives four embryos also pays $11,000. This policy of “moderate”top-up prices

(gMT ) leads to 85% more patients initiating IVF than under gN , and 62% more patients who ever

40For example, a patient with Z = Z who transfers 2 embryos experiences increases in her twin and triplet risksby 12 and 0.3 percentage points, respectively. Each change in risk is multiplied by the corresponding difference inmedical cost relative to a singleton birth.

43

experience a birth during the sample period. While total insurance plus medical costs are 68%

greater with gMT relative to gN , the per-birth medical plus insurance cost is only 3.3% greater.

9.2 Insuring outcomes

To highlight the scope of potential IVF policies and the impact of dynamics in this procedure, we

study two outcome-focused insurance policies. In policy gIO, we again expand insurance to the

full population, but now with unlimited attempts at IVF for patients with one or fewer children

when beginning a treatment cycle. In general, patients prefer an outcome-based policy that allows

unlimited tries relative to treatment-based policies like gIT that insure only a limited number of

cycles. A dynamic model is needed to compare the welfare benefits of gIO and gIT , given their

specific details. From the patient’s perspective at the beginning of treatment, the entire surplus

difference depends on how insurance coverage changes after the first cycle. From a cost perspective,

the key tradeoffs are between delivery costs (which are large when twins and triplets occur) and

treatment costs (which are large when many attempts are needed until success). Insured-outcome

policies might lead to more attempts with less chance of twins and triplets because forward-looking

patients can be more conservative in their embryo transfers. Insured-treatment policies may drive

up delivery costs as forward-looking patients try to succeed in the early (covered) attempts by

being more aggressive in their treatments.

In the second outcome-focused policy we add age-based eligibility conditions, which are moti-

vated by age-related fertility differences, as younger patients are typically more likely to succeed

than older ones.41 Patients under gIA who begin a cycle younger than age 35 receive the full ben-

efit of gIO, while patients with ages between 35 and 40 pay prices halfway between the uninsured

price and the insured one. (This amounts to a discount of about 35%.) Patients age 40 and above

are completely excluded from insurance. This policy has an impact on dynamic decision-making

because it becomes less generous when the patient crosses certain age thresholds, therefore encour-

aging patients to try to succeed before aging-out of the policy benefits. If patients accelerate their

treatment attempts, the age-dependent policy may generate some cost savings as the attempts

are conducted when the patient is younger and more fertile. Therefore, success is more likely to

be achieved in fewer attempts. On the other hand, incentivizing patients to succeed before they

41There are some some similarities between our age-related policy experiment and the dynamic public financeliterature’s treatment of age-dependent tax policies (e.g., Weinzierl, 2011). Just as productivity differences by ageimply that age-related tax policies can be optimal, age-related fertility differences suggest opportunities for policyvariation along this dimension.

44

cross the age-based eligibility thresholds could increase costs if patients become more aggressive. In

addition, patients who speed up treatment experience a utility penalty because they may deviate

from their preferred treatment spacing across cycles.

While policies tied to cumulative patient outcomes and ages may place some record-keeping

demands on insurers (especially if an individual changes providers), this is no more complicated

than current Illinois policy, which requires tracking the cumulative number of cycles.

The treatment-focused policy gIT and the outcome-focused policy gIO have virtually identical

effects on patient initiation, the probability of one or more births per patient, patient surplus, and

insurance costs. The strong similarity between the two policies occurs because very few patients

under gIO choose to take five or more cycles. In the eyes of most patients, the two policies are

similarly generous. This outcome was not guaranteed, and indeed if gIT covers fewer than four

cycles this treatment-based policy provides significantly less patient surplus than gIO.

As expected, the policy with age-adjusted benefits, gIA, has lower overall benefit to patients.

Although older patients are most sharply affected by these limits, the differences in surplus and

costs between gIO and gIA are not especially large. The older patients who would start treatment

under gIO but not gIA are also the patients most likely to fail, so the share of patients with a birth

falls by about 16% while insurance costs for treatment decline by 26%. Overall, treatment and

birth costs fall by more than patient surplus.

Comparisons across patient ages offer the best opportunity to examine differences between gIO

and gIA. In Figure 10 we graph the differences in expected value by age from initiating IVF

for the first time. The largest difference in value is between ages 35 and 40, when insurance’s

price benefit is reduced but not zero. Although the total reduction in price benefit is greater for

patients above age 40, the reduced likelihood of a birth at these ages dampens the value difference

between the policies. It is interesting to note that patients younger than age 35 also have a lower

expected value of initiating treatment under gIA. This is due to cycles after age 35 being subject

to the reduced price benefit. Note that if patients were myopic, the two policies would have the

same value for patients initiating before age 35. The dynamic effects of gIA are also apparent in

simulated treatment histories for patients who initiate treatment between ages 33 and 35. Among

patients who take more than one cycle in total, the average number of quarters between treatments

is 6.0 under gIO, but the patients under gIA delay 5.3 quarters on average. A similar reduction in

delay occurs for patients who initiate between ages 35 and 40.

45

10 Conclusions

Healthcare policymakers face the challenge of designing policies that simultaneously improve access

to care and contain costs. These challenges are particularly acute in the market for IVF, where

treatment is costly, outcomes are uncertain, and there is substantial variation in insurance coverage

for the procedure. A variety of policies have been proposed to address these issues, ranging from

universal insurance mandates to cover IVF, to restrictions on treatment choice in the form of em-

bryo caps. To investigate the impact of these and other policies on patient welfare, outcomes, and

healthcare costs, we estimate a structural dynamic model of the treatment choices made by infer-

tile women undergoing IVF. Our framework incorporates important mechanisms influencing these

decisions, including patient preferences, the evolution of patient health, IVF treatment technolo-

gies, and financial incentives. In addition to the treatment initiation decision, our model highlights

the key tradeoff faced by women undergoing IVF: More aggressive treatment choices increase the

likelihood of a birth, and so reduce future treatment costs, but also increase the possibility of

potentially undesirable higher-order births. We apply the model to a unique dataset of women

undergoing IVF treatment at a major clinic in the St. Louis, Missouri, area between 2001 and

2009. The clinic is situated such that it draws clients from both the Illinois side of the St. Louis

metro area, where IVF is covered under a mandated insurance benefit, and the Missouri side, where

it is not. Consequently, patients being treated at the clinic face very different financial incentives.

Counterfactual simulations from our model show that a universal mandate to cover IVF sub-

stantially increases patient welfare by increasing IVF use. However, the mandate also increases

both treatment and birth costs. We find similar results for an outcome-based policy that insures

births as opposed to treatment. Embryo caps have been proposed as a way to reduce the relatively

high rates of expensive multiple births associated with IVF. We find that a policy of single embryo

transfer (simultaneous with insured treatment) does indeed substantially lower aggregate costs, but

this reduction is largely due to a reduction in patients who initiate treatment. Due to low birth

probabilities with an embryo cap, the total cost per birth is greater than when no patients have

insurance. In addition, our estimates imply that patients receive positive utility from twin births,

which are limited under the embryo cap.

Given that neither unrestricted universal insurance nor embryo caps achieves the dual goals

of increased access and lower per-birth costs, we propose a “value-based” policy in the spirit of

Baicker et al. (2013) and Einav et al. (2016) in which all patients receive insurance coverage for

46

the transfer of a single embryo, but then must pay a top-up price of $12,000 - $19,000 if they wish

to transfer additional embryos. These prices are chosen to fully internalize the expected medical

costs of more aggressive treatments. This policy generates more patient surplus than the embryo

cap or the no-insurance baseline, and insurance plus medical costs are lower than the no-insurance

baseline as well. In addition, there is room to reduce the top-up prices below their fully internalizing

level in an effort to increase patient surplus while still achieving significant cost savings.

Our study of IVF has several contributions for other areas of health economics. We emphasize

the importance of how future treatment opportunities affect today’s choices, which is also impor-

tant in several diseases with long-term treatment strategies, such as heart disease and cancer. Our

consideration of top-up prices is relevant for insurance policy in areas where patients may have

discretion over treatment approach, which can be particularly important in areas where compro-

mises must be struck between patients’utility and other medical concerns or costs. Finally, our

framework illustrates the benefits of using a welfare approach to evaluate policies which may be dif-

ferent in structure (e.g. treatment- or outcome-based insurance) or different in goals (e.g. patients’

surplus or number of births).

The favorable outcomes of the top-up price policies naturally leads to a question of why these

contracts have not yet emerged in the real world. To understand this, it is important to distinguish

between plans offered by insurers under a mandate, versus offerings by insurers not subject to a

mandate. In a setting without mandates, adverse selection and unravelling could result in individual

insurers being unwilling to offer unilaterally any plans with IVF coverage. Our results show that,

in principle, insurers could be better off under a mandate which allows them to coordinate offering

coverage for IVF access while encouraging less aggressive embryo transfer behavior through embryo

caps or top-up prices.

47

Appendix A: Distribution of Types Among Potential Patients

After estimating the model of decision making within the clinic, we know θ =(ϕ, ζ, ρ

)and therefore

W(ZDa0 , τ , gE , ϕ, ζ

). We also know

Pr(τ = 2|ZDa0I = 1, ρ

)= Λ([1, ZDa0 ]ρ). (13)

In addition, from the treatment initiation model we know, for each possible µ (zr) and ZDa0 , the

race-specific initiation rate among potential patients of each type. That is, we know

Λ(W(ZDa0 , τ , ϕ, ζ

)− µ (zr)

)for τ = 1, 2 and zr = 0, 1 (14)

For each ZDa0 we also know the total (i.e. unconditional on type) number of women of each race

with other demographic characteristics ZDa0 who came into the clinic. Let this number be NclinZDa0

(zr) .

Together with Pr(τ = 1|ZDa0 , Ii = 1,ρ

)we then have an estimate of the race-specific number of

patients of type 1 with characteristics ZDa0 who came into the clinic, say NclinZDa0 ,1,zr

(ρ) , where

N clinZDa0 ,1,zr

(ρ) = N clinZDa0

(zr)×[1− fτ

(τ = 2|ZDa0 , I = 1, ρ

)]. (15)

Similarly for type 2, we know:

N clinZDa0 ,2,zr

(ρ) = N clinZDa0

(zr)× fτ(τ = 2|ZDa0 , I = 1, ρ

). (16)

Note that while N clinZDa0

(zr) is data,[N clinZDa0 ,1,zr

(ρ) , N clinZDa0 ,2,zr

(ρ)]depend on ρ, which is identified

by the differential behavior of the two types in the (within-clinic) patient histories. Recall that

ρ parameterizes the within-clinic distribution of types and is estimated in our second step with

(ϕ, ζ) .

Given µ (zr), from the initiation model we know that 100×Λ(W(ZDa0 , τ , ϕ, ζ

)− µ (zr)

)percent

of potential patients of a given race, with additional initial non-biological states ZDa0 and type τ will

choose to initiate treatment. We also know that there we predict N clinZDa0 ,τ ,zr

(ρ) patients of type τ .

Then it must be the case that the number of potential patients of each type, with that combination

48

of demographic states ZDa0 and for that race is given by

N infZDa0 ,1,zr

=N clinZDa0 ,1,zr

(ρ)

Λ(W(ZDa0 , τ = 1, ϕ

)− µ (zr)

) =N clinZDa0

(zr)[1− Λ([1, ZDa0 ]ρ)

]Λ(W(ZDa0 , τ = 1, ϕ

)− µ (zr)

) , and (17)

N infZDa0 ,2,zr

=N clinZDa0 ,2,zr

(ρ)

Λ(W(ZDa0 , τ = 2, ϕ, ζ

)− µ (zr)

) =N clinZDa0

(zr) Λ([1, ZDa0 , zr]ρ)

Λ(W(ZDa0 , τ = 2, ϕ, ζ

)− µ (zr)

) . (18)

Then we can estimate the unconditional (i.e. not conditional on I = 1) prevalence of type 2 among

potential patients of that race with state ZDa0 as

fτ |zr(τ = 2|ZDa0

)≈

N infZDa0 ,2,zr

N infZDa0 ,1,zr

+N infZDa0 ,2,zr

=

1 +

1−Λ([1,ZDa0 ]ρ)

Λ(W(ZDa0 ,τ=1,ϕ)−µ(zr))Λ([1,ZDa0 ]ρ)

Λ(W(ZDa0 ,τ=2,ϕ,ζ)−µ(zr))

−1

. (19)

Note that for given µ (zr), everything in the RHS is known, so fτ |zr(τ = 2|ZDa0

)is known and so is

fτ |zr(τ = 1|ZDa0

)= 1− fτ |zr

(τ = 2|ZDa0 , zr

). If, for a given race, both types were to select into the

clinic at the same rate (i.e. they do not really have different preferences for children), we would have

W(ZDa0 , τ = 1, gE , θ

)= W

(ZDa0 , τ = 2, gE , θ

)so

Λ(W(ZDa0 ,τ=1,θ)−µ(zr))Λ(W(ZDa0 ,τ=2,θ)−µ(zr))

= 1 and the distribution of

types within the clinic and among potential patients would be the same, fτ |zr(τ = 2|ZDa0 , I = 1

)=

fτ |zr(τ = 2|ZDa0

), which is not consistent with our estimates.

Appendix B: Approximating N inf and fZD(ZDa0)

To obtain a model-predicted IVF initiation rate among potential patients of each race we must

use an estimate of fZD|zr(ZDa0). Note that since the expected value of initiation depends on ZDa0 ,

the distribution of ZDa0 among patients who initiate differs from the distribution among potential

patients. In particular, we expect active patients at the clinic to be older, more likely to be covered

by insurance, wealthier, and less likely to be African American. To approximate fZD(ZDa0)among

potential patients we use the following assumptions:

• Assumption 0 (Exogenous ASRM Guidelines). The particular ASRM guidelines in

place are independent of everything else in the model:

asrm ⊥(ZB, ιa0 , zw, a0, zr

). (20)

49

• Assumption 1 (Conditional Independence). Conditional on age at initiation, the 3

biological state variables related to infertility, ZB, are independent of insurance, wealth and

race:

ZB ⊥ (ι0, zw, zr) | a0. (21)

Note that Assumption 1 and the fact that the value of ZB only becomes observable after

deciding to start a first cycle, imply that these variables will have the same conditional (on

age) distribution in the risk set and in the clinic:

f(ZB|a0

)= f

(ZB| a0, I = 1

). (22)

• Assumption 2 (Surprise). Individuals only become aware of their infertility at age a0.

Therefore, the joint distribution of wealth and insurance coverage among women at a0 should

be independent of whether they have any infertility problem (i.e. independent of whether they

are among the potential patients or not). Therefore, Pr (ιa0 , zw, zr|a0) is the same regardless

of whether a woman is a potential patient or not. We further assume that Pr (ιa0 , zw, zr|a0) =

Pr (ιa0 , zw, zr) for all a0.

Using these assumptions we can approximate the joint distribution of all state variables among

potential patients as fZ (Za0) = fZ(ZDa0 , Z

B)

= fZB(ZB|ZDa0

)fZD

(ZDa0).

First note that by Assumptions 0 and 1, fZB(ZB|ZDa0

)= fZB (ZB|a0) = fZB (ZB|a0, I = 1) and

we can easily construct an estimate fZB (ZB|a0, I = 1) using patient data. So we only need to focus

on fZD(ZDa0), which is the critical input for the share-matching procedure described in Section 7.2.

By Assumption 0,

fZD(ZDa0)

= fa0,ιa0 ,zw,zr (a0, ιa0 , zw, zr) fasrm(zasrma0

). (23)

To estimate fa0,ιa0 ,zw,zr (a0, ιa0 , zw, zr) we note that

fa0,ιa0 ,zw,zr (a0, ιa0 , zw, zr) = fa0,ιa0 ,zw|zr (a0, ιa0 , zw|zr) fzr (zr)

= fa0|zr (a0|zr) fιa0 ,zw|zr (ιa0 , zw|zr) fzr (zr)

Distribution of age among potential patients. We first estimate fa0|zr (a0|zr) using data

from the St. Louis region on (first) births and the maternal age associated with those births, by

50

race. Also because of Assumption 2, this gives us the distribution of age at first attempted birth

(regardless of whether the attempt was successful or not) when combined with estimates of race-

specific infertility rates by age. This provides the race-specific age distribution for our potential

patients.

Joint distribution of IVF coverage and wealth. Finally we collect data on the joint dis-

tribution of IVF coverage and wealth, (ι, zw) conditional on race. To estimate fιa0 ,zw|zr (ιa0 , zw|zr)

we consider

fιa0 ,zw|zr (ιa0 , zw|zr) = fιa0 |zw,zr (ιa0 |zw, zr) fzw|zr (zw|zr)

fιa0 |zw (ιa0 |zw) fzw|zr (zw|zr)

and develop a strategy at the zip code level for estimating fι (ι|zw) and fzw|zr (zw|zr) using in-

formation from zip codes whose center is located within 75 miles from our clinic. To estimate

fzw|zr (zw|zr) we assume patients from same zip code are homogenous regarding (ι, zw). In par-

ticular, we know whether each zip code in the St. Louis area is considered “wealthy” or not by

construction: we defined zw,l = 1 if zip code l’s median home value is above $100,000. This is

consistent with the way we are defining a patient to be “wealthy”or not (i.e. whether she comes

from a zip code where the median home value is above $100,000). We estimate fzw|zr (zw|zr) by

fzw|zr (zw = 1|zr) =∑l∈STL

I {zw,l = 1}{

P zrl∑m∈STL P

zrm

}(24)

where P zrl is the population of a given race (zr) in zip code l within the St. Louis region. We have

the population by race for each zip code, so we can construct P zrl easily.

To estimate Pr (ι|w) we take the following steps. We have the percentage of population who have

private insurance for each zip code l within the St. Louis area: fpriv (privl). We obtain this from

the 2012 American Community Survey (ACS) 5-year estimate. A 2005 Mercer Survey of Employer

Health Insurance reported that 19 percent of those with large (500+ employees) employer-provided

health insurance have IVF coverage, and 11 percent of those working for small employers do so.

We assume the same rates apply to Missouri zip codes. We then use estimates from Census’s

Business Dynamics Statistics as reported by Moscarini and Postel-Vinay (2012) and estimate the

employment share of large employers to be 48%.42 Therefore we use the following adjustment

42See Table 1 in Moscarini and Postel-Vinay (2012)

51

factor ψMO = 0.52 × 0.11 + 0.48 × 0.19 = 0.15 to adjust the raw insurance coverage rates we

obtain from ACS. Then the IVF coverage for each Missouri zip code l is given by fIV F(ιIV Fl

)=

fpriv (privl)× ψMO.

Regarding Illinois counties, we know that there is a mandate. But small employers (< 25

employees) and self-insured employers (regardless of size) are excluded.43 According to a Kaiser

Family Foundation (2007) report, 55% of workers nationally are covered by plans that are partially

or fully self-insured.44 So we adjust the raw county-level employer-sponsored health insurance

coverage rate by the percentage of large employers and the percentage not self-funded and assume

that no firm with less than 25 employees provides IVF coverage. We obtain the following adjustment

factor for Illinois counties ψIL = (0.215× 0 + 0.785× [0.45× 1 + 0.55× 0.19]) = 0.435. Then the

IVF coverage for each Illinois zip code l is given by: fIV F(ιIV Fl

)= fpriv (privl)× ψIL.

We then compute the aggregate IVF coverage rate for the region conditional on wealth. First,

we condition on zw = 0 and compute

Pr (ι = 4|zw = 0) =∑l:wl=1

fIV F(ιIV Fl

)( πl∑l:wl=1 πl

). (25)

Regarding coverage conditional on high wealth (zw = 1) we take a different approach. Since most

of the wealthy zip codes are on the Missouri side but ψMO is very low relative to ψIL, if we pool zip

codes together in the aggregation we would end up with a spurious negative correlation. Therefore

we compute Pr (ι = 4|zw = 1) in the following way:

Pr (ι = 4|zw = 1) = Pr (ι = 4|zw = 0) + ∆,

where

∆ =

(∑l:wl=1,l∈IL πl∑l:wl=1 πl

)∆IL +

(∑l:wl=1,l∈MO πl∑

l:wl=1 πl

)∆MO. (26)

43Under this alternative definition of small employer, we interpolate the numbers in Moscarini and Postel-Vinay(2012) and find that 21.5% of employment is accounted for by firms with less than 25 employees.

44We assume that in these self-funded plans the same rate found in the Mercer survey (19%) for large employersapplies. This is probably an upper bound because large employers here also include firms with 25 to 499 employees,not just those with 500+ as in the Mercer study definition.

52

∆s provides the estimated average increase in IVF coverage observed for state s when one moves

from poor zip codes to wealthy zip codes within that state.

∆s =

∑l:wl=1,l∈s

fIV F (IV Fl)

(πl∑

l:wl=1,l∈s πl

)− ∑l:wl=0,l∈s

fIV F (IV Fl)

(πl∑

l:wl=0,l∈IL πl

)for s = IL, MO. The results indicate that IVF insurance coverage rate depends of wealth. Among

poor potential patients, 83% have ι = 0 and 17% have ι = 4. For wealthy potential patients, 75%

have ι = 0 and 25% have ι = 4.

Size of Potential Patient Pool. In addition to the joint distribution of characteristics among

potential patients, we need the size of the potential patient pool N inf . We use N inf to refer to

all potential patients in the St. Louis area, and N inf for the subset who might consider the clinic

we study. We count the race-specific number of women of each age in the St. Louis region that

give birth naturally to a first birth in any given quarter. Let this number be Na,zr , which we

obtain from Vital Statistics. The total number of women who attempt their first pregnancy at

age a is N stla,zr . Of these, Na,zr succeed and have births recorded in Vital Statistics; the group

that fails, N infa,zr , contributes to our set of potential patients. Therefore N

stla,zr = Na,zr + N inf

a zr .

Then using infertility rates by age and race among women who are attempting to get pregnant,

inf (a, zr) , we back out Ninfa,zr = inf(a,zr)

[1−inf(a,zr)]Na. According to Vital Statistics, the larger counties

in and around the St. Louis region have an average of 1172 first births each quarter distributed

among mothers aged 28 to 44. To capture births occurring in the more rural areas, but still within

our 75-mile radius area, we also estimate the births occurring in smaller counties within this area.

An additional 10.4% of births come from these counties.45 So N75m28−44 = 1172×1.104 = 1294. Using

infertility rates by age and race and summing across ages, we can then determine that there are

N inft = 257 × 1.104 = 284 new potential patients, on average, each quarter.46 Since there are 28

quarters between 2001 and 2007, the size of the potential patient pool for our sample period is then

N inf2001−07 = 28× N inf = 28× 284 = 7944. While this pool of potential patients is valid for the full

St. Louis area, our clinic has market share sclin < 1. According to the CDC, the clinic we observe

45Births occuring in smaller counties are combined and reported into a single residual county for each state inVital Stats. So we know how many first births occured in these “residual”counties. We also know how important (interms of number of households) the zipcodes belonging to small counties but located within the 75-mile radius areas a share of the each state specific residual county. Therefore we can augment the number of births in the relevantarea by assuming that the same share of births comes from these zipcodes.

46To obtain age-specific infertility rates inf (a, zr), we interpolate between ages 28 to 39 and extrapolate for ages40-44 the 12-month infertility estimates reported in Dunson et al. (2004) and adjust these estimates using relativerates of infertility between black and white women from based on data from NSFG.

53

has market share of about a third, and we adjust N inf2001−07 in a proportional way. Ultimately the

potential-patient population for our clinic is N inf = 2781. Of these, 486 are black and 2295 are

non-black.

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57

58

Figure 1: IVF treatment stages

Note: We display patients’ immediate payoffs at each stage of the decision tree, and include expected future payoffs only where the patient has reached the end of a within-period decision sequence. We omit some notation to avoid clutter.

If already initiated

Delay Start

Learn # eggs (r)

No ICSI ICSI

Cancel Continue

Learn embryos (X)

Choose x ≤ X

us – αps,1 εd,1 + βEW1(Za+1)

εnc,2 + βEW1(Za+1)

Go to next period

Go to next period

εc,2 – αpc,2

εm2,3 – αpm2,3 εm1,3

Σ𝑘𝑘>0𝑓𝑓𝑘𝑘(𝑘𝑘|𝑥𝑥)�𝑈𝑈�𝑘𝑘�𝑘𝑘� , 𝜏𝜏� + β4𝐸𝐸𝑊𝑊1(𝑍𝑍𝑎𝑎+4)�+ 𝑓𝑓𝑘𝑘(0|𝑥𝑥)β𝐸𝐸𝑊𝑊1(𝑍𝑍𝑎𝑎+1) + ε𝑥𝑥,4

Go to next period

Learn Peak E2

Stage 1 / Period start

Stage 2

WOUT = µ + ν

Stage 3

Stage 4

If at initiation decision

Learn ZB

No initiation Start εs,1

59

Figure 2: Distribution of Peak E2 Outcomes by AFC

Figure 3: Distribution of Retrieved Egg Count by Peak E2

0.1

.2.3

0-500 500-1000 1000-1500 1500-2000 2000-2500 2500+

Low AFC High AFC

0.2

.4.6

1-4 5-10 11-20 21+

Low Peak E2 High Peak E2

60

Figure 4: Distribution of Embryos Available by ICSI Use, Male Factor Patients

Figure 5: Distribution of Births by Embryos Transferred, Patient Age 34-36

0.2

.4.6

.8

0 1 2 3 4+

No ICSI With ICSI

0.2

.4.6

0 1 2 3

2 Embryos 3 Embryos

61

Figure 6: Distribution of Births by Patient Age, 3 embryos

Figure 7: Predicted Stage 4 Decisions on Embryos Transferred

0.2

.4.6

0 1 2 3

Age < 35 Age 35+

0.1

.2.3

.4.5

0 1 2 3 4

Observed Predicted

62

Figure 8: Embryo Transfer Choices in Counterfactual Experiments

Notes: N = No insurance. IT = Universal insurance for treatment. AT = Insurance plus actuarially fair top-up prices. MT = Insurance plus “moderate” top-up prices.

0.2

.4.6

.81

0 1 2 3 4

N IT

0.2

.4.6

.81

0 1 2 3 4

N C

0.2

.4.6

.81

0 1 2 3 4

N AT

0.2

.4.6

.81

0 1 2 3 4

N MT

63

Figure 9: Births Outcomes in Counterfactual Experiments

Notes: N = No insurance. IT = Universal insurance for treatment. AT = Insurance plus actuarially fair top-up prices. MT = Insurance plus “moderate” top-up prices.

0.2

.4.6

.8

0 1 2 3

N IT

0.2

.4.6

.8

0 1 2 3

N C

0.2

.4.6

.8

0 1 2 3

N AT

0.2

.4.6

.8

0 1 2 3

N MT

64

Figure 10: Difference in Patient Expected Value at Initiation between IO and IA

Notes: Vertical axis plots difference between expected value from policy IO (Universal insured outcome) minus IA (Insured outcome with age-adjusted benefits.

01

23

4EV

diff

eren

ce

30 35 40 45Initiation age

65

Table 1: This Paper’s Clinic in Context

This Paper’s Clinic All U.S. Clinics

Number of cycles per year 370.2 217.1 Patient median age 34 35-37 (see note) Patients with 2+ infertility diagnoses 11% 12% Male partners with infertility diagnosis 18% 17% ICSI use 50% 59% Embryos per cycle 2.41 2.68 Birth rate per cycle 33.5% 29.9%

Note: We use our main data sample to calculate patient median age for the clinic we study. For all other statistics we use the annual summary data published by the CDC for the clinic we study and the U.S. as a whole. In the CDC’s data patient ages are reported in intervals.

66

Table 2: Patient-level Characteristics

Main sample First-stage sample

N = 587 N = 1106 Mean Std. dev. Mean Std. dev.

Demographic state variables (ZD) Patient age at initiation 34.30 4.02 33.31 4.70 Insured at initiation? (Y = 1) 0.54 0.50 0.59 0.49 Wealthy zip code? (Y = 1) 0.82 0.39 0.79 0.41 Prior children at initiation 0.00 0.00 0.30 0.56 African American? (Y = 1) 0.05 0.21 0.05 0.21 Biological state variables (ZB) AFC score 14.37 7.96 14.61 8.13 Female fertility problem? (Y = 1) 0.80 0.40 0.69 0.46 Male fertility problem? (Y = 1) 0.34 0.48 0.30 0.46

Aggregate actions and outcomes Total cycles 1.75 1.02 1.97 1.21 Birth during sample period? (Y = 1) 0.53 0.50 0.55 0.50

The “Main sample” is used in second-stage estimation of patients’ choices. The “First-stage sample” is used to estimate treatment technologies.

67

Table 3: Actions and Outcomes within Treatment

Main sample First-stage sample

N Mean Std. dev.

N Mean Std. dev.

Stage 1-4 actions

Cancel treatment? (Y = 1) 1027 0.14 0.35 1859 0.14 0.35 Fertilization method? (ICSI = 1) 879 0.60 0.49 1597 0.59 0.49 Number of embryos transferred 875 2.29 0.81 1592 2.32 0.82

Stage 1-3 outcomes

Peak E2 score 1027 16.82 9.73 1905 17.19 9.77 Eggs retrieved 879 10.60 5.46 1697 10.87 5.60 Embryos generated 881 6.11 3.75 1687 6.34 3.86 4+ embryos? (Y = 1) 881 0.74 0.44 1687 0.76 0.43

Stage 4 outcomes

Children born 848 0.51 0.70 1632 0.55 0.75 Singleton birth? (Y = 1) 848 0.27 0.45 1632 0.27 0.45 Twin birth? (Y = 1) 848 0.12 0.32 1632 0.12 0.33 Triplet birth? (Y = 1) 848 0.00 0.00 1632 0.01 0.10

The “Main sample” is used in second-stage estimation of patients’ choices. The “First-stage sample” is used to estimate treatment technologies.

68

Table 4: Utility Parameter Estimates

Utility of 1 birth (u1) 5.143 Price sensitivity constant (α0) 0.312

(0.928) (0.070) Utility of 2 births (u2) 5.866 Price sensitivity X wealth (αw) -0.127

(1.682) (0.066) Utility of 3 births (u3) -14.095 Terminal payoff 0.228

(4.411) X Prev. payment (γ) (0.631) Utility shift when 𝑘𝑘� > 0 (κ) -11.868 Utility shift from beginning -4.909

(0.956) treatment (δ) (0.098)

Preference shifter ζ 9.768 Penalty for violating ASRM -3.036

(0.865) embryo guidelines (η0) (0.194)

Standard errors are in parentheses.

Table 5: Utility-Type Distribution Parameter Estimates

Constant (ρ0) -1.269 Insurance (ρ3) -0.017

(0.552) (0.367) Age (ρ1) 0.041 ASRM regime (ρ4) 0.469

(0.013) (0.340) Wealth (ρ2) -0.864 Race (ρ5) -1.032

(0.457) (0.879)

Standard errors are in parentheses.

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Table 6: Initiations, Cycles, and Outcomes across Policy Settings

Policy setting (g) Share initiating N cycles if initiate Share with birth N births N infants

Empirical Baseline (E) 0.299 1.348 0.159 456.2 636.4 ( 0.295, 0.305) ( 1.280, 1.445) ( 0.148, 0.173) ( 422.1, 496.8) ( 584.6, 691.1) Insured treatment policies No insurance (N) 0.242 1.277 0.127 360.7 505.2 ( 0.227, 0.258) ( 1.204, 1.396) ( 0.113, 0.145) ( 321.3, 413.3) ( 446.0, 576.4)

Universal insurance 0.577 1.426 0.315 902 1245.2 for treatment (IT) ( 0.512, 0.625) ( 1.365, 1.507) ( 0.281, 0.347) ( 808.0, 997.5) (1114.0,1373.0)

IT + embryo cap (C) 0.287 1.238 0.077 217.9 247.4 ( 0.226, 0.342) ( 1.127, 1.357) ( 0.061, 0.093) ( 172.7, 263.4) ( 197.2, 300.6)

IT + actuarially fair top-up 0.323 1.271 0.113 320.5 397.7 prices (AT) ( 0.280, 0.373) ( 1.181, 1.396) ( 0.100, 0.130) ( 282.3, 371.6) ( 349.0, 476.7)

IT + moderate top-up 0.449 1.356 0.206 586.7 778.8 prices (MT) ( 0.407, 0.485) ( 1.297, 1.461) ( 0.183, 0.231) ( 523.6, 656.1) ( 688.6, 881.5) Insured outcome policies Universal insurance 0.576 1.412 0.311 883.2 1210.8 for outcomes (IO) ( 0.511, 0.625) ( 1.353, 1.494) ( 0.277, 0.343) ( 788.9, 980.1) (1081.9,1336.5)

Age-adjusted insurance 0.484 1.4 0.278 787.6 1087.9 for outcomes (IA) ( 0.442, 0.517) ( 1.337, 1.486) ( 0.251, 0.307) ( 712.6, 869.7) ( 979.2,1194.9)

95% confidence intervals are in parentheses

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Table 7: Surplus and Costs across Policy Settings

Policy setting (g) Total surplus in risk population ($M)

Total IVF insurance cost ($M)

Total medical delivery cost ($M)

Medical cost per birth ($000)

Insurance + medical cost per

birth ($000)

Empirical Baseline (E) 10.3 3.6 31.4 68.9 76.9 ( 8.3, 13.7) ( 3.1, 4.0) ( 28.6, 33.9) (66.9, 69.5) ( 74.4, 77.7)

Insured treatment policies No insurance (N) 7.6 0 25.0 69.4 69.4 ( 5.6, 10.8) ( 0.0, 0.0) ( 21.8, 28.5) ( 67.0, 70.0) ( 67.0, 70.0)

Universal insurance 18.4 16.4 60.5 67.1 85.2 for treatment (IT) ( 16.0, 22.4) ( 14.6, 18.0) ( 54.4, 66.8) ( 65.9, 68.2) ( 84.4, 86.2)

IT + embryo cap (C) 5.6 7.3 8.5 38.9 72.4 ( 4.4, 7.4) ( 5.7, 8.8) ( 6.8, 10.4) (38.8, 39.7) ( 71.8, 73.8)

IT + actuarially fair top-up 7.8 8.3 11.9 37.1 63.1 prices (AT) ( 6.0, 11.4) ( 7.3, 9.7) ( 10.5, 13.8) (36.0, 38.4) ( 59.4, 66.2)

IT + moderate top-up 13.3 12.2 29.9 50.9 71.7 prices (MT) ( 10.5, 17.9) ( 11.1, 13.7) ( 26.1, 34.3) (48.4, 52.7) ( 70.4, 72.7) Insured outcome policies Universal insurance 18.5 16.2 58.3 66.1 84.4 for outcomes (IO) ( 16.0, 22.6) ( 14.5, 18.0) ( 52.4, 64.4) ( 64.9, 67.2) ( 83.6, 85.4)

Age-adjusted insurance 15.7 12.0 52.7 66.9 82.1 for outcomes (IA) ( 13.3, 19.6) ( 10.7, 13.3) ( 46.8, 57.5) ( 65.2, 67.7) ( 80.5, 82.8)

95% confidence intervals are in parentheses